That's a good point. We live in a world of mobile broadband cards. I don't know what Ireland has in regards to them, but the ISP in that way would be in space wouldn't it? And in that situation it would become a case by case basis. It'd be kind of funny if the only website still around during the zombie apocalypse was purple.com.
Of course the odds of discovering that would be pretty random. Still...if this fella has any government ties, I'm sure he could log into a government only server which would be around for some time.
I wonder if the zombie apocalypse would be anything like a nuclear apocalypse. I mean those underground fallout shelters would do wonders to stop the zombie invasion assuming that people weren't initially bitten when they went in. Course you'd have to worry about survivalists maybe...although the odds of them finding you would probably be pretty slim. But then you really couldn't rely on a mobile broadband card in a vault either...interference.
Hmmm...
How awesome would a story be about the zombie invasion and all the main character is concerned about is seeing a book trailer on YouTube though. XD Those godforsaken squirrels have eaten the interwebz! What am I to do?!?
So I think if you're going to make a logic tree for the problem it would be something like this...
Zombie Web 2.0
|
ISP
|
Cable
DSL
Satellite
Cable Internet comes from a cable service provider. It utilizes space on a designated channel for data transmission.
DSL is kinda crazy. The further you are from the central office, the slower your internet becomes. The limit is somewhere around 5,460 meters or 18,000 feet. Because customers at the end of the extreme might receive MUCH lower download speeds...most providers actually lower that distance between centers.
Apparently I am naive and I was thinking mobile broadband came from satellite. It comes from the same radio towers that cellphones use. European towers broadcast a different radio signal called GSM or HSDPA (High-Speed Downlink Packet Access) It is unique because it allows voice and data transmissions to be performed at the same time. Now there is satellite internet available in western europe. I believe it is called Tachyon. The way THAT works is that information is sent from the Hub to the satellite in space and then from the satellite beamed down to your own personal satellite at your home. It deals with both downloads and uploads. However it does have its limitations. Preferably your satellite should have a clear view to the south and should be in an area free of trees, buildings, etc. Rural areas mostly.
Alright...
So here would be my reflections:
Cable television and phone lines would probably be down pretty quickly. For one thing...telephone lines would probably be off the hook, experiencing incredible stress due to the fact that everyone is trying to warn family members, call the police, ambulance, etc...
Plus people on the road...are probably going to be pretty reckless and as such if the phone lines are above ground...there is a good chance someone is going to hit the pole when trying to avoid traffic or zombie attack. It seems like if you stick a random pole in the ground people go after it like a moth to the flame. Seriously...think about how many drunk drivers end up hitting a power line or phone line...weird.
Cable television will be kept going as long as there is someone alive to produce the news. However I think the trouble with that would mostly be that the government, if capable, will probably be taking control of the networks in order to produce calming propaganda. Electricity will go out and buildings will lose power.
Cellphone towers will be experiencing extreme levels of use during the beginning of the apocalypse. When power goes out...mobile broadband cards will not receive a signal.
Satellites will be up in space. However they will be silenced when the hubs go down and are no longer transmitting information.
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Now...the aftermath:
Satellites might be the easiest way to establish an internet link should you be able to supply the terrestrial ones power. Also...the chance of any repairs during the zombie apocalypse would seem unlikely...although there is always a chance a plane might go down on one.

There are probably some pretty crazy satellites set up all over the place. The government might have some set up for emergencies in places that provide their own natural power (such as the Hoover Dam in the US?). Might be the stuff used in a story, but...how would a character even know where that existed unless they were pretty high in the military or political hierarchy?
Cellphone towers might also be relatively safe, but again, you'd have to head over there remotely and activate them. Both of these are assuming that you have a way to supply power (such as a generator) and even then someone would have to remain to make sure that they were up and running. And of course not only that, but you'd have to have fuel for the generator.
I'm of course overly simplifying things. I have no idea what sorts of computer software or know-how that you would need in order to get one of those things up and running again.
Cable and DSL lines seem pretty tricky to me. They're made to supply phone systems and video after all. If you can fix all that...well heck...you'd have your own little city wouldn't you? You probably wouldn't really need the internet in that case. It would be funny if the person found a way to get some kind of cable network programming working, but were forced to only have reruns of I Love Lucy to watch.
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And then of course...assuming you got all those systems up and running...the internet is based off of a bunch of networked servers. Once the power is wiped out on their end...you do not have any more websites. I would think that this would probably go before everything else.
The government might have a network...perhaps a gigantic network that backs up all of the websites that maybe google scans or so...just for the sake of archiving Earth's history. Do they do that? I don't know. I know that there is a website that apparently does since you can go look at AOL's website from 1991, 92, etc.
If that's the case a person could reestablish the Internet...but really...what purpose would the average Joe have in doing that? It's not like he's going to go online to pizzahut.com and order himself a pizza for delivery.
...I think it'd be easier to use a CB or some kind of ham radio or maybe even get a radio station up and running for communication than the Internet.
Pretty much when all the electricity in the world starts failing...that is going to be the end of the Internet as well. Unless of course you have some nuclear reactor that someone is keeping pretty maintained. But I think most people, if alive, are going to be more interested in getting out of Dodge and to the mountains or on some kind of sea barge or make their castle a maximum security prison than worry about whether or not Oprah is still alive on entertainmentweekly.com