I have the same problem and here are my PC’s specs:

homebuilt
MB: ASUS AV8 (has sound and lan)
CPU: AMD Athlon 64 3000+
VC: ASUS Radeon A9550 128MB (AGP)
RAM: 2x 512MB PC3200 Azenram

OS: Vista Business with SP1 (not running eye candy, just as classic windows)
Router: D-Link DGL-4300

Software installed:
Adobe Flash Player ActiveX
Adobe Flash Player Plugin
APC PowerChute Personal Edition (for my UPS)
avast! Antivirus
Classic Menu 3.x for Office 2007
Creative WebCam NX Pro Driver (1.03.03.0326)
Free eXPert PDF Reader
Microsoft Office Professional 2007
Mozilla Firefox (2.0.0.14)
Realtek AC’97 Audio
SpamPal
Spybot – Search & Destroy
Windows Live installer
Windows Live Messenger
Windows Live Sign-in Assistant

And to re-iterate the problem and symptoms:
After the system has been on for a while, browsing will suddenly stop in both IE and Firefox but IM will continue to work. Browser will indicate website found, waiting for reply and will wait but never show the page cannot be displayed. Unable to access 192.168.0.1 from a browser. Only a reboot fixes the problem and it comes back after some time.