As an experiment, try opening Gmail in a private window. Private windows use a separate set of "this session only" cookies so any cookies you still have should not be a factor.

To open a new private window, either:

• Ctrl+Shift+p
• orange Firefox button (or File menu) > New Private Window

Does Gmail working normally in that window?

It is possible that the cookies.sqlite file that stores the cookies is corrupted if clearing cookies doesn't work.

Rename (or delete) cookies.sqlite (cookies.sqlite.old) and delete other present cookies files like cookies.sqlite-journal in the Firefox profile folder in case the file cookies.sqlite got corrupted.

• http://kb.mozillazine.org/Cookies
• https://support.mozilla.org/kb/Deleting+cookies