It won't be the router. If the problem rights itself after rebooting the COMPUTER, then the problem can't be with the router (as a hardware problem)

For the problem to be the router, rebooting the computer wouldn't make fuck all difference. You'd need to reboot the router or swap out the LAN cable to a different port. I had a router randomly drop ports - ie my machine would be plugged into LAN 1 and work fine, then one day not work at all. Swapping to LAN 2 would solve the issue.

So it's either a software issue on the PC (problem with the network card or IP assigning) or an ISP problem as t31ryt says.....

EDIT - have you done anything with phone line recently? Have you a microfilter in each socket?