Zero seconds.

Sorry :)

The problem is the word "All" in your question. You can cut the power, cut the phone lines, cut the fibre. Some people on the town are still going to have satellite uplinks and private generators. You then also need to cut off all mobile phone networks and prevent anyone from hovering an air mast over the town.

The internet was designed from the very start to be resilient and route around failures.

If you are willing to accept occasional individuals having access to the internet still (and for some reason them not being willing to share) then it gets a little simpler as you just need to take out the major internet hubs into and out of the town. In a sufficiently isolated town that could be as simple as a digger accidentally going through the wrong cable although most places have redundant connections. You could argue that the mobile networks go through the same cables to explain them going down as well.

The repairs to that would normally only take a few hours to days, but a sufficiently bad storm or blizzard might delay that causing the outage to last until the weather improved.

I think the only thing that even comes close to what you are looking for is a massive electromagnetic storm (solar flare?) that is disrupting all advanced electronics. Something like a continuous low grade EMP. It would fry computers and mobile phones but allow more primitive electronics to survive.

Explaining that without it also knocking out the power grid and/or taking out the whole planet is tricky though.

A good answer will explain the series of events that causes the town to lose power

Apparently this American isolated farming town has been without electricity for ten months and counting, as one data point.

Fortunately or unfortunately, losing power is probably neither necessary nor sufficient for losing Internet.

As an alternative, I'll offer the North Korean Solution: a brutally-oppressive government blockade. Even this might have some problem with satellite telephones, but turning all the jamming up to 11 is probably an option.

The town could be located in the United States National Radio Quiet Zone, a region of approx. 13,000 square miles in West Virginia, Virginia, and Maryland. Radio transmitters of all kinds are heavily regulated within the zone, to facilitate scientific and military installations in the area.

Cellular service is apparently restricted to nonexistent within the region. There is little to no broadcast television or radio; residents generally rely on cable or satellite television. it's plausible for satellite Internet service to be prohibited because it requires the subscriber to transmit to the satellite.

Aside from the radio restrictions, that part of the country is mountainous and economically depressed. Laying data cables through forested, mountainous terrain is difficult and expensive, and the local utilities may have trouble funding a network built to modern expectations. So the kind of robust infrastructure that you might find in other parts of the country--redundant communication links, with armies of technicians standing by to repair outages--might not exist in the region.

Finally, the area's status as a radio quiet zone apparently attracts people with Electromagnetic hypersensitivity, a "claimed sensitivity to electromagnetic fields". So the region may have an unusually high number of people who avoid computers, cell phones, and the Internet as a matter of course.

One could imagine a community within the region that's completely dependent on a few terrestrial cables for phone and data services. The local telephone company and cable provider really ought to lay some backup cables, but they've been skimping on that because the customer base is too small and too poor.

Then comes an earthquake, a big forest fire, or a lot of rain, triggering a huge landslide. A slide which takes out the terrestrial cables. Virtually nobody has satellite or cellular Internet because they're in the quiet zone. Even if someone wanted to bring in some portable satellite links, microwave stations, or cellular towers, they can't because a lot of the roads and bridges in the area were also wiped out. On top of that, the electrosensitives in the community could start harassing anyone operating a transmitter. There might even be electrosensitives on the city council or other positions of power.

It could easily take a week or two to get the town hooked back up. It could take even longer if the disaster which cut the data links was something widespread, or if some of the people operating the utility, local government, or other positions of power had reasons to slow down the process of reconnecting the town.

I believe Centralia has little to no incentive for companies to invest in networking infrastructure there:

Centralia is a borough and near-ghost town in Columbia County, Pennsylvania, United States. Its population has dwindled from more than 1,000 residents in 1980 to 63 by 1990, to only seven in 2013—a result of the coal mine fire which has been burning beneath the borough since 1962.

Wouldn't be surprised to learn that you can't get even cell phone signal there.

You may also consider places like Puerto Rico:

Puerto Ricans are by law citizens of the United States (...) In late September 2017, Hurricane Maria made landfall in Puerto Rico, causing devastating damage. The island's electrical grid was largely destroyed, with repairs expected to take months to complete, provoking the largest power outage in American history.

There was a lot of talk about how and why the grid took eleven months to be restored, but if I start to rant on policticians and toilet paper we are bound to have things edited out.

An isolated farm town could rely on diesel generators for power, so cutting off the Internet means cutting broadband as well as phone access. A simple event, such as the bankruptcy of their local ISP and phone carrier, is all that it takes. But life can go on for most of the residents for a long time. They still get newspapers delivered from big cities in their states, they get deliveries of oil and spare parts, they pay quarterly IRS taxes at the post office, and they rediscover the joys of reading novels and playing board games. They can even take selfies with their Polaroid cameras while children play Fortnight with paint guns.

Quite a long time, if you define "internet" as "internet good enough to provide the services most westerners associate with the internet".

Now, of course there will be some satellite internet users with generators who are very hard to cut off. But the top voted answer forgets about something: Satellite internet is slow and really expensive. It depends on where you live, when I wrote this answer I had speeds for Africa in mind. But it's also expensive and slow in the USA, just not quite as expensive and bad. And it varies by location within the USA, so you should be able to find a place with bad coverage.
There is no such thing as a flat rate, you pay by volume (or it's a "flat rate" but they cut off most of the bandwith if you use too much). Most Americans wouldn't be able to afford enough of it. They would share one connection among lots of friends and that connection would only be good enough for email and the like. Very few people could afford to browse a site like this one for fun, and it would be slow as hell. No one would pay for the download of a movie or lots of pictures - it would be much cheaper to have it shipped to you, even from far away and paying for express shipping.

And to get to that state, as mentioned by other answers, you could

• Cut off the couple of lines (at most, one is plausible) that connect the town to the outside using a mudslide, accidental damage during construction work, gas pipe explosion, sinkhole, etc.


• Could be complicated by archaeological or historical findings, discovery of old waste dump (can become really nasty with chemicals, fires, water contamination if not approached correctly), discovery of radioactive material, discovery of poisonous natural resources, or anything similar near the accident site. If the town is small enough and the damage large enough then no one will be in a hurry to rebuild because it wouldn't be that lucrative.


• Because of the previous items or some other reason the only provider in town could go bankrupt, with some legal battle drawing out the proceedings and keeping other companies from buying the lines. This is quite plausible in the USA, I think, because I doubt the government would do anything to help.

It's completely sufficient to cut the landlines to cut mobile internet - mobile internet doesn't reach that far and it's based on the same physical network.

To maximize the downtime, you'll want a failure that takes an unreasonably long time to fix. It doesn't have to be complicated, just time-consuming.

For example, say your town is at the edge of a network, connected to the rest of civilization by a single underground data cable. An equipment failure on one end sends a huge surge of electrical current down the wire, heating it up to the point where insulation melts and the wire shorts itself out in multiple places along its length. Repairing the cable isn't really feasible, it has to be replaced. That means replacement cabling has to be ordered, miles and miles of old cable has to be dug up, new wire has to be laid, trenches filled, and tests run. This is a slow, labor-intensive process that can take weeks (or longer, depending on the distance to the town, terrain, etc).

Like most things in life, getting the government bureaucracy involved will help maximize the amount of time required to repair the problem. Not only do you have to re-trench all of that line, but the cable runs through three different counties. That's three separate sets of permits that you have to get. Since you cross county lines, you have state-level paperwork that you have to file as well. And you can't even start any of that until the regulatory agencies finish investigating the original equipment failure. The relevant government officials are busy campaigning for the next couple of months (it is an election year after all), but they should be able to start on your paperwork by the next fiscal quarter or two...

This can easily leave your other utilities intact (if you want them to be), as they can be run on separate lines. I know, you're probably asking What about:

• 
  Mobile Internet access? - Due to terrain (such as being in a valley surrounded by hills with high iron content), wireless connections to neighboring areas aren't reliable. Mobile phone traffic gets routed over the existing, now-dead Internet connection. After the failure you could still have mobile phone service, but only for calls within the city.


• 
  DSL connections? - The phone network in this area is an old-fashioned, twisted-copper-pair infrastructure, good for simple voice calls but nothing beyond that. The phone company never built the infrastructure required for providing data services because it is just a simple regional co-op that can't break even without state subsidies (not uncommon for rural/isolated areas). Your landline phone can still work, but no Internet here.


• 
  Cable Internet? - Due to the isolation factor and the cost of running cables back to the next town, the local cable provider received its programming via a satellite link (which should still work fine). Your cable provider was also your local ISP, but the Internet signals were routed through the cable which is now dead. The cable company's satellite connection is one-way, so re-routing Internet traffic through it isn't practical.


• 
  Satellite Internet? - Many commercially-available satellite Internet services aren't true "satellite" connections. The consumer's equipment is capable of receiving signals from a satellite (downlink), but isn't capable of transmitting data back up to the satellite (uplink). Instead, the uplink is handled by a terrestrial connection such as dial-up or mobile wireless (all of which are down). You'd still technically have a working downlink, but the Internet doesn't really work with one-way-only connections. True two-way satellite connections exist, but they're expensive, and no service provider may yet exist in this area. Also, your local regulatory agency may not allow citizens to broadcast signals in the required frequency range, due to potential interference with critical infrastructure.


• 
  RFC1149 protocol communication? - This would technically still work. However, the latency is horrendous, and packet loss is a major problem. Not yet reliable enough for practical use.

A situation like this could easily buy you several months' worth of time without a real Internet connection. There are always extreme solutions that someone could come in and implement to restore a limited connection for critical purposes. The key to preventing those is cost vs. return. Upgrading the infrastructure to support DSL or a two-way satellite link for the cable company would be a straightforward and relatively quick solution, but would be prohibitively expensive in most cases given the limited size of the customer base (they'd never make their money back before the more-cost-effective cable gets repaired). As long as waiting for the main connection to be repaired is the most efficient solution, then that's what people will do. Maybe it's one of those projects that's perpetually three weeks from completion but constantly suffers delays. Or maybe the local ISP has a state-protected monopoly, and it's actually illegal for anyone else to offer Internet service through any other means.

If the city's utilities, emergency services, etc are all still working fine and the lack of Internet is merely an inconvenience, then people will adapt and wait it out. After all, it wasn't that long ago that Internet access was uncommon, particularly in rural areas.

On February 3, 2021, the sun abruptly launched a ball of plasma directly towards Earth. Traveling at nearly 1% the speed of light and weighing about as much as Manhattan, the world would spend the next 18 hours preparing for the coming storm...

A coronal mass ejection aimed squarely at Earth would knock out both terrestrial and satellite communications. Power would also likely be knocked offline but is more easily repaired, especially if the town has its own power plant with locals to make the repairs. Densely populated areas would recover quickly, but more rural areas could take months to recover. Depending on how much you consider the aftermath of such a cataclysm to be "life as normal", you could have your town offline for days, weeks, or months. You can also make the town particularly vulnerable by putting it closer to the poles, where the storm's effects would be stronger.

I'm surprised no other answer mentions it

Earthquake

A powerful earthquake can do a lot of damage. A land mass is moved, often by meters efficiently breaking all continuous infrastructure lines, including optic fibre, copper cables and so on. The strength of the quake can also put down any microwave mast that provides communication. Of course it means also power outage and all other means of communication (mobile phones) down plus problems with water, gas etc.

This will not disrupt the satellite service but a small city like this might actually not have anyone with such communication. Even if actually does have, those will be just few people and as already mentioned in other answers the connection is painfully slow and costs arm and leg.

The power restoration (to some degree) will be fast - there might be some local power plant, people will use spare power generators, some might be equipped with solar panels. Yet it might not be able to operate for long (except solar panels) due to fuel shortage that cannot be resupplied quickly due to road damages.

Of course once such event happens there will be steps taken to resume as much service as possible, yet the power, water and gas will be priorities. It will definitely take weeks if not months to restore internet service at a reasonable level through standard means (first optic/fibre then build new masts).

On the other hand in case of such events there is a solution called Loon to provide via balloons a temporary, mostly uninterrupted internet connection to an area cut off of a normal communication. You can imagine that such disaster will cause looking for a ways to provide as much help and support as possible nationwide so this will be launched for sure. Effectively the internet downtime will be at the level of 1, maybe 2 weeks. After that time it'll be restored using Loon and after 1 to 3 months there will be enough temporary infrastructure to provide a more or less normal (even though limited) service via traditional means.

In rural areas a total blackout for every last person would be almost impossible. There are many places around here that have their own power generation and satellite uplink.

I, myself, live in a rural area and my TV and internet are satellite and I run solar cells for my own power.

People in the closest town are on fiber or copper based internet as well as mobile internet.

For everyone to go out, too many seperate things need to go wrong.

Best you can do it to have a whole town go out due to a fiber being cut or a tower going down but even then for a city of 50K people, there will be multiple backups.

Take a look at the mid-2000s TV show Jericho, which was about the titular fictional small town Kansas community trying to survive after being cut off from outside communication following the detonation of Nuclear Devices in several major U.S. Urban Centers. They actually cut off the city in two very distinct and different ways in the first season alone. The initial attack cut off several network connections and long distance resources. Since most American Media (even local news) is broadcast from major cities to various regions, this knocked out most media coverage of what happened almost instantly (in fact, the first hint of trouble was the sudden town wide interruption of a Presidential Address to a Joint session of Congress... before the Mushroom cloud over the nearest major city was seen. They only learn of the extent beyond a regional issue from a boy in the town who has a voice message from his parents at the moment of detonation while they were in another city). For much of this portion of the season, power in the city was still on (and in fact, electricity was the cause of a fire that threatened the town a few episodes later).

The second problem occured at the Mid-Season hiatus, when the episode ended with the launch of nuclear missiles presumbably by the United States against an unknown enemy... on of the missiles did something that caused an EMP to blow the entire power-grid of the town, essentially putting the town's facilities back by 100 years for a good portion of the show (they do get a generator that restores some services).

Edit: In a city of 50,000 people and located near an interstate like the example of Grand Island there is practically very little except for a power outage that could wipe out Internet service.

However, if you reduce the size of the city and place it in the mountains far away from an Interstate or major roadway and large city there are a couple of ways to cut most or all Internet service to that town.

First let's look at the physical ways people get Internet and cell phone service.

1) Fiber optic cables

2) Copper wires/cables

3) Cellular

4) Microwave

5) Satellite

Fiber

Let's say the town is isolated, perhaps in a canyon you can eliminate the fiber option because unless there is a major business or super wealthy individual the infrastructure is too expensive.

Copper

Copper wires are pretty old technology and only support low speeds over long distances and would have long ago been replaced with microwave comms.

Cell Service

Since the town is not near any major roadways and pretty far away from other towns, setting up cell towers all the way out to this town would also be cost prohibitive. Cell service would most likely be brought in via microwave with a cell tower or two placed around the town for coverage.

Microwave

Microwave comms has been around for decades and can hop tens of miles per tower so that is a very likely scenario - many places to this day use microwave towers to provide telephone and other services.

If you take out one tower the town is out of comms for as long as it takes to construct another tower with the proper comms gear. Weather, truck accident, sabotage - there are many ways to take out a single tower. Especially if the towers are on mountain tops in rugged terrain. A significant storm could cause a landslide that should make erecting another tower take a significant amount of time so that a proper location could be scouted. Telephone, cell phone, Internet would all travel over this one microwave link and thus take out all communications other than satellite.

Satellite Comms

Natural - A solar storm could easily knock out a couple of satellites - so too could a piece of debris in orbit.
Sabotage - Satellite signals are quite weak by the time they reach the ground. If someone set up a transmitter with even moderate power on the satellite bands, it could easily jam incoming signals.

That takes care of the physical hardware but there are other single points of failure.

Problems with the single Internet Service Provider:

1) The company could go bankrupt

2) The ISP could have a fire, flood, explosion, etc. at the 'edge' node that goes to the town.

3) A group of hackers could compromise the edge node.

And just for good measure, here is a real life example of a fairly large group of people losing their Internet for a short time.

Verizon told me on June 3rd that the fiber was part of a ring that
stretched from New York city through Broome County. The other side of
the ring was taken out the day before by a manhole fire and was under
repair. No Verizon services were affected. Once the other side was cut
on Thursday by stormy weather, Verizon and First Energy, who they
leased the fiber from, had to wait to the all clear from the utility
and emergency services to repair the break.

For as long as you want

In the middle of the 1990, polish science-fiction author Stanisław Lem wrote an essay and stated in several articles and interviews how he saw the internet as a dangerous risk. His prediction was that one day, when most of human technology and culture depended on the internet, one or a group of computer viruses would incapacitate or even completely destroy the internet, destroying civilization as we know it. His view was considered extreme, but if you remember the extent of WannaCry, imagining a concerted attack on the internet infrastructure no longer seems such an impossibility.

For your story, all it takes is bringing down one or two network nodes, not even the whole of the internet. Look at a map of the internet, and you will soon find many places that rely on only some few mainlines to keep them online. And since often many or all nodes in a certain region are owned by a single provider and therefore all run with similar hard- and software, taking all nodes in a certain region (and only there) down, would get you the result you need.

Here is a list of real world internet outages and their causes:

https://en.wikipedia.org/wiki/Internet_outage

There is an option nobody here seems to find.
And it even leaves the citys power supply intact.

The ISPs have joined up to screw with the city

thats the only reliable way to make it happen.

In Europe thats hardly thinkeable, but in the US, especially rurual areas, the cell coverage provider and the cable ISPN are often the same, so its not hard to picture a town 100% reliable on Verizon for example.

Now, if either Verizon decides that that town deserves to be screwed with OR if for example Verizon infrastructure gets hacked, destroyed or infected with the right virus, that town is done.

Especially if the interruption is voluntary and initiated by Verizon itself for maybe legal reasons, the whole thing could take months to resolve, especially if Verizon has a good reason to drag it out.

Eventually someone will buy a satellite phone, but you can ignore that one guy

As a resident of one of those three cities you mentioned, I am genuinely curious how this would work out.

For starters, you would definitely have to get rid of the marketing departments for every ISP in town; they're quite proud of the uptime around here. But I digress...

Perhaps a localized pop-culture EMP?

They may not do exactly what you're looking for, but depending on how much fudging you're willing to do, you might be able to cause suspension of disbelief.

Good luck, regardless.

I'll be waiting for the network to go out with a bunch of paperbacks and a basement full of canned goods.

Really you can keep them without Internet access for as long as you want, but it's going to have to be via making sure they've got more important things to do than restore the service.

"The Internet" is nothing more than a mesh of interconnected communications channels that happen to span the globe. You can run an Internet link over ANY communication channel. Fiberoptic cables are the most common thing used for covering long distances these days because they are both cheap and fast, but as others have mentioned, you can also use satellite dishes, and cell phones.

I'll add a few more:

• Consumer-grade wireless relays (5 mile hop distance with a properly-constructed, narrow-beam antenna)


• Telephone Lines


• Blinking lights: https://en.wikipedia.org/wiki/RONJA
  


• HAM radio (Or any other kind of radio transceiver set with varying ranges and data capacity)


• Carrier pigeons: https://en.wikipedia.org/wiki/IP_over_Avian_Carriers#Real-life_implementation
  


• Human couriers.


• Telegraph lines (using Baudot code or even encoding the data down to International Morse Code.)


• Guys on the mountain tops waving semaphore flags: https://en.wikipedia.org/wiki/Semaphore_Flag_Signaling_System
  

You can even transmit data between computers just using their built-in sound cards and microphones. This is impractical for long distances, but has been used for attempting to exfiltrate data from secure systems.

Now, some of these are obviously going to be extremely low throughput, extremely high latency, or both. Some of these are going to be expensive to run. This won't prevent them from working, but it will limit what kinds of Internet resources it may be practical to access. Simple, text-only email would work reasonably well over any of them though, and that could be used to coordinate delivery of information or goods via some other, bulk channel.

So, in short, to cut them off from the Internet, you need to cut them off from ALL communication channels with the outside world, and keep them too distracted with their own problems for them to bother re-establishing any.

For real-world examples, look at some of the conflicts in the middle east over the last ten years or so where the governments have tried to shut down the country's Internet access in an attempt to impede dissident groups from coordinating their attacks. Even with the government actively hunting and turning off rogue uplinks they were unable to keep it suppressed for more than a few hours at a time.

Obligatory XKCD: https://xkcd.com/705/

Unless it's a metropolis, there will usually be one, at most two fiber cables (well bundles of fiber cable) going to a city. Depending on how desolate the region is, they might even still have copper (though I doubt it).

Mobile internet usually works by the transmitting tower being either connected to the same fiber cable, or being in a wireless mesh topology, landing in the same fiber cable after a few hops. Or mobile internet not working at all because, well you know, you're on the country side!

Depending on how retarded your provider's infrastructure is, you'll have a physical or logical ATM network in addition to IP as well, but finally it's all the same cable bundle. Cut the cable, and it's dead.

Next are sattelites. One-way sattelite internet, somewhat out of fashion nowadays, without the cable providing control flow, is useless. Nothing to be done.

Two-way sattelite internet would be an issue, but not so much really. The only serious, no-joke provider that I know (with more than a few dozen kilobits per second) that serves north America would be Viasat. Though I'm pretty clueless because sattelite internet isn't too important to me, personally, so there might be more.

But either way... how many sattelites can there possibly be that you'd need to deactivate or destroy, 5 or 6? Should be no issue.

Someone with enough power (think government) or enough criminal energy might even do it without cutting the cable or going anywhere near the city. Just deactivate the router where the cable leaves the IXP/CIX, and send "line down" commands to some sattelites (or deactivate a subset of subscribers, the sattelite can as well serve others, why not), done.

Thinking of it, cyber-warfare comes to mind...

So that leaves a few elderly geeks who might transmit over CB at a couple of hundred bauds. Is anyone still doing that at all? This is sooooooo 1980.

Uh, well, let's not consider that possibility. This counts as "no internet"!

The town is doing it on a bet.

In the 1971 film Cold Turkey, a tobacco company offers $25 million dollars to the first community to stop smoking for 30 days. The intent is for the company to gain the PR benefits of offering the prize, without actually paying out the money because no town could possibly give up smoking for that long.

An economically depressed town in Iowa decides to go for the prize. Everyone in town signs a no-smoking pledge or else leaves town for the duration. The rest of the film follows the town as it struggles to last out the full 30 days.

Now, what's the smoking addition of the 21st century? Why, Internet addiction, of course!

MyFacePage Inc., the world's largest social media platform, is under attack on several fronts. Too many people are addicted to the Internet and it's affecting peoples' health and productivity. People also think MyFacePage is too big and should be regulated or broken up.

MyFacePage wants to clean up its public image, while secretly giving everyone an object lesson in how the world can't do without them. So they pretend to care about Internet addiction and offer a bazillion dollars to the first town which can give up all Internet access for 30 days or whatever period you like.

Some economically depressed town takes them up on it. The city council manages to talk the townspeople into going along with it. They use their regulatory oversight with the cable, telephone, and cellular providers to disable data access (or maybe they don't; maybe the whole town is on the honor system).

Few if any residents have satellite Internet, because it's normally a last-ditch option and wouldn't be common in areas that (formerly) had perfectly fine Internet service. Beyond that, they might be able to get a waiver from the FCC (the head of which is in MyFacePage's pocket) allowing them to temporarily ban satellite Internet. Or they could rely on social pressure to control it.

I live about 40 miles from Grand Island, NE.

Where I'm from, "GI", as we call it, is a real city. It's the big town, providing support many other rural areas, but it's not exactly a farming community. They have industry of their own separate from farming, and I'm there myself to do some shopping every other month or so. The town I live in is significantly smaller than Grand Island (only about 7,000), yet is itself large enough to be a commercial center for other smaller communities going through at least 15 miles of farmland or more in every direction.

Even out here in the sticks, I have multiple options for internet service. I've had broadband service provided by Windstream and Time Warner (now Spectrum). From tracerts, one of those follows a line leaving the state through Lincoln, while the other routes through Denver (I don't recall which is which at the moment). My employer has service through a private fiber deployment company that ultimately runs through Lincoln, but arrives in town on a completely different right of way from the other Lincoln service. I also have a friend who works in IT with the local bank, and I know they have service through a fourth provider.

And these are all fiber-backed services, though none of them yet do fiber to the home out here. That said, those four providers are all there is, and they don't have much redundancy. A single misplaced back hoe can cut fiber and take out service for a significant portion of the state... but only for a few hours. Taking out a major interconnect point in Lincoln could do even more. A major event there could leave me and others without service for significant time.

This doesn't even bring up cell service. Verizon, AT&T, Sprint, and US Cellular all claim to offer service here (though AT&T doesn't actually work in a meaningful way). Verizon does have decent data service here, and while their towers are generally fiber-backed, I believe they have the capability to backhaul via tower to tower wireless links if need be.

If that fails, we've still got old-fashioned dial-up, which can be used to jump start some basic satellite internet. Many communities here also rely on fixed-point wireless, where an enterprising soul will contract with a fiber provider for a gigabit or two backbone, put some ubiquiti radios up on a mast, and use them to sell service to truly rural farms that couldn't get it otherwise. One of those providers in a neighboring community would surely be able to link up something to your target town.

The upshot is completely cutting off everything is gonna be real difficult. You're talking coordinated attacks on multiple fiber trunks and cell towers, or a major event at an interconnect point big enough to cause a lot of collateral damage to other communities of less interest to your story, even in farm country.

However, things become more interesting if you start looking at real farming communities. My wife has an aunt and uncle in such a community in rural Arkansas, population roughly 200. We were there for Thanskgiving just last week, and you don't need a special event to take service down; there isn't any service to begin with. Even the nearest Verizon cell tower seems to turn the signal strength down at 8pm on the nose every night. They consider themselves lucky to have satellite TV.

For as long as there aren't any devices capable of connecting to the internet

As other questions have pointed out, to take down access to the internet would be all but impossible. The remaining option is to remove the devices that enable connecting to the network.

This could happen several different ways but essentially you need some motive for a large proportion of the town to start searching for and destroying all devices. These motives could be anything from being convinced any device emitting a signal could cause cancer (a common complaint but apparently without much merit) to a belief that the internet is turning the citizens from religion, the spread of the unknown can lead to drastic action by those afraid of losing the world they knew.

Once these devices are gone then you're without any ability to access the internet. Sure you could say they would miss some...but that is up to you and how you write the story. This approach, at least, isn't impossible.

They live surrounded by mountains and they all access the internet via a repeater mast high up on one of them. None of them have satellite because the service from the repeater has always been so reliable. Take the repeater out and there you are.

EDITS

If anyone does have satellite then you will also have to take out the local ground station(s).

Satellite Internet generally relies on three primary components: a
satellite, typically in geostationary orbit (sometimes referred to as
a geosynchronous Earth orbit, or GEO), a number of ground stations
known as gateways that relay Internet data to and from the satellite
via radio waves (microwave), and a small antenna at the subscriber's
location.
https://en.wikipedia.org/wiki/Satellite_Internet_access

However - At the moment I believe all such satellites are in geosynchronous orbit. If that's the case then a mountain could simply block the part of the sky where the satellite is. GS satellites are always around the equator because they must match the spin of the Earth so in the US the satellite would be to the south.

Better be quick though because new configurations of lower orbits satellites are planned.

There may be holes in my arguments and so more research is probably desirable. I just put the idea in case it's a useful lead.