I'm not sure about the internet as it exists today, but there could still be data transfers. Since software defined radio, there have been a lot of interesting

I'm not sure about the internet as it exists today, but there could still be data transfers. Since software defined radio, there have been a lot of interesting things happening in the HAM radio world. You can share information around the world using radio waves. There's even a project to stream video. It's possible to make your own cell tower, so it might be possible to build a cellphone network. Provided the people that can do it don't get eaten :P