Webpages stop displaying after 5-10 minutes, rest of Internet still works

This is semi complicated. I'm not sure what else I can do.
About 5-10 minutes after a restart, Internet Explorer and Mozilla can no longer view web pages. Any other connections I make such as email, IRC, online games, ftp, software updates, all work perfectly. There is also another computer sharing the modem, and it has no problem connecting to anything.

What I know:

1. I have run Ad Aware, and Spy Bot, and a couple different anti-virus programs, and they have found nothing.

2. No extra processes are running, but when I restart with a third party firewall, I don't have this problem (I connect to webpages as normal.)

3. When I restart without the firewall, and run TCP View, several processes appear with the TIME_WAIT state that never appear when the firewall is active. A capture of TCPView with these connections here: http://www.geocities.com/sxnrr/TCPview.jpg (top 4 connections)

I have spent days trying everything I can to fix this problem. Any help would be great.