Make an entirely new profile, I bet it will work. I'm guessing both the existing profiles have something set that is breaking login. No idea what it can be, unless you explicitly blocked cookies from the domain. Not something that you can do accidentally though.
Yeah I've been down this frustrating route before. Somehow your profile has gotten corrupt. You'll probably never know why.
Has happened to me for Chrome and Firefox. Creating a new profile works. Or if you're feeling paranoid, remove any trace of it from the system and do a fresh install.
