No, no one is shutting down the Internet. Idiot journalists without technical knowledge are once again creating bogus headlines to create fear and panic!
What's going on is that last year, a computer virus was released that changed the DNS setting (see below for quick description). It set up to look up to a bogus server instead, so everytime infected computers went somewhere, they had to (unknowingly) contact the virus' authors. When they were caught, the FBI set up a replacement for that server, so that people would still be able to connect, and to notify them that they are infected.
What is DNS: computers deal with IP addresses (such as 220.127.116.11). That's not very likely that we puny Humans will remember all those numbers, so a system was devised where we could type in "www.google.com", the computer would query a server (the DNS), and return the IP address above. With that address, the computer can now contact Google. The address of the DNS, however, has to be entered somewhere, and this is what the virus changed.
According to this page
, people infected would have seen a warning whenever using Google. All anti-viruses should have been able to detect this virus for a long time now. The FBI has warned a lot of people. In short, if you're still infected, chances are you ignored every warning.
While it is possible that all 4 laptops are infected, it is unlikely that the Wii is infected, because, like a Mac, it doesn't run Windows code, and the virus was made for Windows. The most likely scenario is that the router has the wrong DNS setting. Your Internet provider will be able to supply you with the correct DNS address, but most likely won't be able to tell you how to enter it into your router, unless that "router" is a Windows computer. You're probably best off calling a local computer shop so they can dispatch a tech. I would also recommend having him do a thorough virus & malware scan, because it is unlikely that you have only a single virus.
Edit: just for kicks, go on one of those computers that can't access the net, and type in this address in a web browser: http://18.104.22.168/
You should see the Google page come up. You still won't be able to go anywhere else, but that should be proof that the Internet is still there.