I had a similar problem, where my Mac Mini would connect just fine but my daughter's iMac and my Dell laptop would not. Rebooting the router solved the problem for a little while, but it would recur within minutes. Oddly enough, when I examined the router's settings, I found that the "local time" was January 1, 1970. The internet time server it was using must have gone down, or gone away. I gave it a new time server IP address, and the problem was solved.
Granted, this is a weird one, but it shows that any of dozens of settings might be out of kilter. Try to reset the router to factory settings (usually a paper-clip-reachable switch on the backside of the device.) You might also check Belkin's web site for an update to the router's firmware -- if there is a newer version available, install it.