We had a new Vista machine that did this. Turned out to be the Vista Beam Of Death issue (aka Broadcast Flag.)
While it's rare today you can still encounter the issue.
However how can I tell given the details in your post? Maybe it's something else?
Bob
Hi, I wonder if anyone can advice. I have a vista laptop and pc, I connect both to the internet via a wireless router. The trouble is, is that when one connects to the internet the other one gets knocked off! I'm sure it has something to do with the IP address but I have no idea how to resolve the issue.
Thanks
Bea

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic