I had the exact same problem and did the steps in comment #3 with the exact same results.
So, I tried:
sudo dpkg-reconfigure lightdm
That appeared to resolve the problem once I switched the default display manager back to lightdm.
After that I was able to do:
sudo apt-get purge gdm
And I did not have any problems getting to the login screen with lightdm after that.
I had the exact same problem and did the steps in comment #3 with the exact same results.
So, I tried:
sudo dpkg-reconfigure lightdm
That appeared to resolve the problem once I switched the default display manager back to lightdm.
After that I was able to do:
sudo apt-get purge gdm
And I did not have any problems getting to the login screen with lightdm after that.