I haven't seem many routers fail. The best way to test that though is to connect into a different port (especially since you mention other computers working in your location). Assuming they are hooked into the same router, try one of those connection.
What is more likely though: Sounds like malware to me ( I fix computers for a living). Run a decent program like adaware (
www.lavasoft.com) to check that 1st. Also--check to see what programs are loading up at boot and then watch for other ones that have loaded once your problem starts. Ctrl+Alt+Del to check processes for that. It can be a pain though as there are so many things to track in there.
Try to think about what (if any) changes have occurred recently as well. New Programs loaded? Any goofy shut-down that happened? Dumping TEMP Files is a good idea (browser>Tools>Delete temp files and cookies while you're at it). You can also go Start>Run and type in %temp% and try to delete all the files that are revealed (there may be a couple you can't).
Again--while hardware is always a possibility, this one sure
Feels software related to me...
Good Luck!!!
EDIR: What anti-virus do you use? Any updates to it recently before this started?