I just tried a bit of "surgery" - I made a new installation (from the scratch) into Virtualbox and took all contents of /etc/pam.d and merged it into my main system - the one with this bug - thus overwriting files with new ones but keeping all additional files - not from the system itself - untouched.
And guess what? Everything seems to work WITHOUT these "workarounds" tried before. This implies to the difference in some other file in /etc/pam.d, which is "left over" from 13.04 and causing this problem - other file than /etc/pam.d/lightdm.
I just tried a bit of "surgery" - I made a new installation (from the scratch) into Virtualbox and took all contents of /etc/pam.d and merged it into my main system - the one with this bug - thus overwriting files with new ones but keeping all additional files - not from the system itself - untouched.
And guess what? Everything seems to work WITHOUT these "workarounds" tried before. This implies to the difference in some other file in /etc/pam.d, which is "left over" from 13.04 and causing this problem - other file than /etc/pam.d/lightdm.