It isn't Windows fault (this time)

I fixed the computer that would not remember passwords. It turns out to be something inside Firefox, at least Firefox 3.10. Just this once, Windows is not guilty. Here's how to fix passwords.
On the Firefox Menu Bar click Tools->Options. Click the Privacy tab. Make sure cookies are enabled and "clear private data on exit" is UNCHECKED. Remove any cookie EXCEPTIONS that might block sites you care about. Do Show Cookies and then delete all of them. Sometimes cookies get corrupted which confuses Firefox. Wiping them all out will force the websites to create new, clean cookies next time you visit.
Next click the Security tab. Check "Remember Passwords". Then click on Password EXCEPTIONS. Remove any Exceptions blocking sites you care about. In my case an Exception was blocking Facebook. I have no idea how that Exception got planted, but there it was.
Clearing it allowed me to click right into my facebook page without having to hand type my password each time.