Excuse me butting in but when you untick the keep me logged in box you should the be able to type your own details in from the same screen. it's on the extreme top right. Are you saying you can't do this?
I can type my email address in okay but everytime I log out his email address and password appear. Even after I've put my details in and clicked 'remember me'
It may have been chrome my dad was using but the same thing happened with all of his log ins. He'd always sign out but his username and password would still appear already when he went back to the page.
I had to delve around the browser settings and there was a random option I unticked which fixed it.
Try signing in thru a different path ie via answerbank FB or google whichever is not your usual. When you have a 'clean' sign in, delete your original & reinstall FB