Earlier mention was made about using the Winsock fix. I would point out that if you are at SP2 level then the Winsock Fix is not appropriate and the SP2 alternative should be tried.
WinXP Connectivity Issues
faq779-4625
Did you ever try the Internet Explorer Fix?
Windows XP Internet Programs Cannot Connect to the Internet Through Broadband Connection
If Firefox uses the same Temporary Internet Files folder as IE (I have no knowledge of Firefox) then this may apply?
You receive a "page cannot be displayed" error message when you try to log on to a Web site by using Internet Explorer 6
The check lists in this article are worth following, especially about cleaning out Temp and Temporary Internet Files.
Troubleshoot Situations Where You Cannot Connect to Secure Web Sites by Using Internet Explorer in Windows XP
How to troubleshoot TCP/IP connectivity with Windows XP
How to troubleshoot network connectivity problems
Some general things to try.
See if System Restore will get you back to a restore point before your problem with Explorer.
Run the System File Checker program from the Run Box by typing.....Sfc /Scannow in it and have your XP CD handy.
If they don't work you could try repairing windows by running it over itself. You will lose all your windows updates but your files will be untouched.
How to Perform an In-Place Upgrade (Reinstallation) of Windows XP (Q315341)