Per Mozilla support, the user data isn't deleted when Firefox is uninstalled using Add/Remove Programs. So, when the program is reinstalled, perhaps it loads the previous profiles instead of creating a new one? And perhaps the problem lies within the profile rather than the program?
You can try starting Firefox in safe mode or w/ a new profile.
Maybe try to create a new profile in Firefox and see if you can access GMail that way? I think when a new profile is created, you'll start off w/ default everything. Just a thought.
Click Start > Run, type Firefox.exe -profilemanager
Save your FF bookmarks to a flashdrive then use http://www.revouninstaller.com/
to remove FF & then go to Start>search >All files & Folders & search for FF there. Delete what is found & then hopefully you can reinstall FF & start fresh.
I have found out from experience revo doesn't uninstall everything all the time
I've heard alot about FEBE but never had any luck using it which is why I save mine to a flashdrive.
I'll check it out to see if its any easier,thanks.