Try the Firefox SafeMode to see how it works there.
A troubleshooting mode, which disables most Add-ons.
Troubleshoot Firefox issues using Firefox SafeMode

When in Safe Mode...

• The status of plug-ins is not affected.
• Custom preferences are not affected.
• All extensions are disabled.
• The default theme is used, without a persona.
• userChrome.css and userContent.css are ignored.
• The default toolbar layout is used.
• The JIT Javascript compiler is disabled.
• Hardware acceleration is disabled.

• You can open the Firefox 15.0+ SafeMode by holding the Shft key when you use the Firefox desktop or Start menu shortcut.
• Or use the Help menu item, click on Restart with Add-ons Disabled... while Firefox is running.

To exit the Firefox Safe Mode, just close Firefox and wait a few seconds before using the Firefox shortcut (without the Shft key) to open it again.

If it is good in the Firefox SafeMode, your problem is probably caused by an extension, and you need to figure out which one.
http://support.mozilla.com/en-US/kb/troubleshooting+extensions+and+themes
Or it might be caused by Hardware Acceleration.

When you figure out what is causing that, please let us know. It might help other user's who have that problem.

Do other input fields on this page work or is this the only that isn't working?

Can you reach this input field via (possibly multiple presses) the Tab key?

You can check out for a problem with the page code by right-clicking in this area and selecting "Inspect Element" to see what gets selected.
It is also possible that there is a JavaScript running on this page that isn't working properly and prevents clicking in that field.

This was not a Firefox problem. I disabled the pop-up blocker and was able to enter the password.

This was not a Firefox problem. i disabled the pop-up blocker and was able to enter my password. Thank you.