Could you try a fake username and password on another site, and see if you can save there? You can use this website's login form at https://support.mozilla.com/tiki-login.php to test.

Let me know the result of doing this, and whether any password-related errors appear in Tools->Error Console

I was given the option to save my pswd.

Do you get the sliding bar at the top? What happens if you click the Remember button?

See also http://kb.mozillazine.org/Password_Manager (Troubleshooting)