Internet problem - websites not working

I'm having a problem with my internet connection on one of our computers (the other one is fine). The problem computer is able to connect to the internet (either ethernet or wireless), but not able to view websites (WoW works just fine, for example). Sometimes if I restart it, everything will work for a few minutes, and then all of the sudden I can't view websites any more. I've tried several things so far and nothing works - I have the same problem even in safe mode with networking. I'm not sure if this is related, but a few days before this happened, I began to have trouble networking the two computers.

My error messages on Firefox sometimes say "Connection interrupted - connection to server reset while web page was loading" and on IE they say "Network timeout"

Dell Optiplex GX260
Windows XP SP3
Speedstream 6520 modem/router
I had avast on it until yesterday when I tried uninstalling it to diagnose the problem

Has anyone seen similar symptoms before? Thanks in advance for your help!