pam_ck_connector(lightdm-greeter:session): nox11 mode, ignoring PAM_TTY :0
A search on the Web suggest that only one user cannot login because, for some reason, ~/.Xauthority is unreadable. A solution would therefore be to log into a text session (Ctrl+Alt+F1 gives one) and remove ~/.Xauthority:
$ sudo rm ~/.Xauthority @amuza: tell us if that solves your problem.