That's some weird problem
.. I'm seriously beginning to wonder if it would be quicker to just copy your docs/videos/firefox profile/etc. to an external drive .. then just reinstall.
Maybe even take this opportunity to move to a more recent version of Ubuntu .. or Mint (MATE) .. or PeppermintOS 3
I'm going to do a bit of research on reinstalling the login tools .. but we could be here forever trying to track down what the problem is .. I *would* ask you to post the logs, but I'm guessing they'd be in Danish (?) and fairly useless to me.
It may work from a USB stick depending on your PC .. some old PC's don't like booting from USB sticks.
Do you know how to burn the ISO image to a USB stick ?