Did you end up here after running sudo startx ? Nevertheless:

Press Ctrl + Alt + F3 and login into the shell.

Now run ls -lA . If you see the line

-rw------- 1 root root 53 Nov 29 10:19 .Xauthority

then you need to do chown username:username .Xauthority and try logging in (you may also need to do the same for for .ICEauthority ).

Else, do ls -ld /tmp . Check for the first 10 letters in the left: they should read exactly so: drwxrwxrwt .

drwxrwxrwt 15 root root 4096 Nov 30 04:17 /tmp

Else, you need to do sudo chmod a+wt /tmp and check again.

If not both, I'd recommend you either

sudo dpkg-reconfigure lightdm or uninstall, reinstall it.