Mint has been working perfectly, now suddenly it wants a password and won't let me login

Yesterday Mint gave warning messages that the root partition has run out of space. I emptied the trash and moved several GB of stuff to another drive. When I booted up today I get as far as the desktop (with nothing on it) and a login window, but when I enter the password the screen blacks out for a moment and goes straight back to the login window.
I have changed the password (getting in via recovery) but that did not help.
This is a dual boot system with Windows 8.1, which I never use anymore.
I have no idea where to go from here, please help.