Please start with; all of your Adobe programs are out of date.

Security Issue: Update your Flash Player Version 17.0.0.169
https://www.adobe.com/products/flashplayer/distribution3.html

See if there are updates for your graphics drivers https://support.mozilla.org/kb/upgrade-graphics-drivers-use-hardware-acceleration

Use this link to check that your plugins are up-to-date. If any are listed as unknown or research, do not worry about them.

This was useful in a way, some of the things listed did needed to be updated, but I still can't log in...

Did this site used to work for you in Firefox, or has it never worked in Firefox?

Do you log in using a site account or one of the other options (Facebook/Twitter/Google)?

After you are returned to the login page, if you go to the home page and reload (Ctrl+r) does it show you logged in? In other words, it would be useful to know whether the problem is a broken redirect or a failed login.

One reason logins can fail is restrictive cookie settings. Those can be caused by changes to Firefox's Privacy options, or by privacy-related add-ons. Could you check this article to see whether your cookie settings allow for the maximum compatibility: Websites say cookies are blocked - Unblock them.

If that doesn't help, could you test in Firefox's Safe Mode? That's a standard diagnostic tool to deactivate extensions and some advanced features of Firefox. More info: Diagnose Firefox issues using Troubleshoot Mode.

If Firefox is not running: Hold down the Shift key when starting Firefox.

If Firefox is running: You can restart Firefox in Safe Mode using either:

• "3-bar" menu button > "?" button > Restart with Add-ons Disabled
• Help menu > Restart with Add-ons Disabled

and OK the restart.

Both scenarios: A small dialog should appear. Click "Start in Safe Mode" (not Refresh).

Any improvement?