I had a similar-ish problem, and changed the router channel and it's been fine since.
To change the channel you need to plug your computer into the router directly, go to
http://192.168.0.1/ and then log in and go through the settings. You'll probably be on channel 6. Try changing to 11 and see if that helps.
Are you on wireless? He said desktop in the OP..
But it's a good point by Boshi. Is there an internet light on your router, and when you have the problem, do you see that light go out?