That issue can be caused by corrupted cookies.

• https://support.mozilla.com/kb/Cannot+log+in+to+websites

Clear the cache and the cookies from sites that cause problems.

"Clear the Cache":

• Tools > Options > Advanced > Network > Offline Storage (Cache): "Clear Now"

"Remove Cookies" from sites causing problems:

• Tools > Options > Privacy > Cookies: "Show Cookies"

• http://kb.mozillazine.org/Cookies
• http://kb.mozillazine.org/Websites_report_cookies_are_disabled

My problem has not been solved. Today another site is having same problem. Please refer the attached JPEG file to resolve my problem.

Can you login if you switch to Private Browsing mode?

• https://support.mozilla.com/kb/Private+Browsing

I am unable to login in private browsing also. Same problem is there.

I see a CAPTCHA on that image of the not easy kind (at least to me).

Are you sure that you entered the code correct?

Start Firefox in Diagnose Firefox issues using Troubleshoot Mode to check if one of the extensions or if hardware acceleration is causing the problem (switch to the DEFAULT theme: Firefox (Tools) > Add-ons > Appearance/Themes).

• Don't make any changes on the Safe mode start window.
• https://support.mozilla.com/kb/Safe+Mode