You can still log on as root from the command line. Since this is a KDM error, it stems from the graphical logon. From that screen, instead of logging on, press Alt-F1 and you will get a command line login prompt. Log in as root and you will have full access to your system.
Look in /var/log for the KDM logfile. Use the
command like you would use dir in Windows. I don't know the logfile name but it should be intuitive. Display the end of it using
If you see the error, you might be able to figure out the solution. Otherwise post the error here and someone can probably help. Unfortunately, you probably can't copy/paste the message into your reply so until you learn some more tricks you will probably have to retype it.
Reinstalling Mandriva would probably work, but becoming involved in fixing it in place would give you a major boost toward understanding the Linux system.