So, i just got a new computer from a friend of mine. It is a couple years old running Vista, but i keep having this problem. I can connect to either of my routers, and i will be fine for about 5-10 mins before it disconnects me from Skype or Yahoo or whatever webpage i am on. The connection icon in the corner doesn't say it is disconnected, but everything disconnects.
So it's not actually a "new" computer then, just new to you, which means who knows what's on it or how it was working before. Make sure all Windows updates were done, check the vendor for any new network card drivers, maybe try a different network cable. If nothing works, re-install Windows.