Sounds like perhaps the winsocks are messed up so one thing you could try if this is a computer with Windows XP with SP2 installed, I am going to assume that this is the case.
1. Click on Start then go to Run and type cmd then enter or click ok to bring up the command prompt.
2. At the command prompt type in "netsh reset winsock catalog" with out the quotes then after a few seconds it should tell you that it successfully reset the catalog and to restart the system.
3. type exit then press enter.
4. Restart computer and try connecting and browsing again.

I have a similar problem and tried the above solution, unfortunately it didn't solve the problem
I am on a home network with DSL connection running through a Linksys wireless access point router. My desktop (vista) is directly connected and the internet is functioning normally on this pc. My laptop (Windows XP SP2) however is giving me some issues. It connects to the network fine and even appears to be connected to the internet, as evidenced by software updating and full functionality of googletalk, however neither IE or Firefox will load any sites. Firefox tells me:
Unable to connect
Firefox can't establish a connection to the server at "whatever site I try to access.com"
-The site could be temporarily unavailable of too busy. Try again in a few minutes
-If you are unable to load any pages, check your computer's network connection.
-If your computer or network is protected by a firewall or proxy, make sure that Firefox is permitted to access the Web.

None of that helped me. I've tried Window's network repair, reinstalling firefox, resetting my router, the solution mentioned above, various other attempted solutions, and I've been looking around these forums for awhile for anything else that might help. Nothing.

If I need to pass on any more information please let me know.