How come in gated communities like Alexandria where there's electricity and normal appliances there is no computer with a wifi connection? Telecomm companies might have been zombie infested but that doesn't explain how or why no one has an internet connection. Furthermore, airports might have stopped operating but it's not like the landing strips aren't there. It's as if they are suggesting all pilots and private jet owners have died or zombified. All those semi-peaceful days in Alexandria you'd think they'd try to get in contact with similar communities around the world and bring civilization and peace back.
Several studies I've read a while ago indicated that it's the internet network which is most resistant to all kinds of disasters. That is not to say that it will stay up no matter what, just that the losses in the infrastructure will be the least of all communication methods and will be easiest and fastest to have it back up.
The Last Ship, for example, featured communications via network of mobile phones with bluetooth (not sure if it wasn't wifi too) to send messages over state lines even. Not much of an example to address your question, but illustrates possibilities.
However, as Gallifreyan says in a comment, there must be someone to maintain the network, and even without that damage would be extensive. I did not watch the series beyond first season (I find all zombie things boring after reading "The Black Tide" series by John Ringo... or stupidly ridiculous like the iBrain or something), but I find remarkably low damage level in it. There should be a lot of buildings burned down, for example, burned cars, destroyed infrastructure, including relay stations and exchange cabs etc. And by a lot I mean at least 50%.
And, of course, satellite network is now sufficiently sophisticated to allow for internet connection. I'm surprised no one really uses satellite phones - you can buy an iPhone add-on to convert it to sat phone for less than $200 (i think), and having a smartphone is half-way-there to the IoT.