I have Mandrake 8.2 set up and when it boots up it boots into run-level 5 (it boots up X and brings up that GUI login window where you can click on your username, type in your password and select the desktop environment you wish to use).

Anyways, tonight I tried logging in and it wouldn't work. I typed in my login name, password, and selected KDE as my desktop; but nothing happened. The screen flicked off and then back on again and it brought up the same GUI login window. I tried restarting X, but nothing seemed to work.

Has anyone else had this problem? Any solutions, other than reinstalling Mandrake?

1st possibility that I can think of, usually ask by helpdesk, 'Did you type your password correctly?'

Yeah, I am certain that I typed the password correctly. Usually if you type in the wrong password or login name it usually just gives you a message like 'Login failed'. But in this case I typed everything in correctly and it restarted X and went back to the GUI login screen.

just make sure that is it a password or a kdm problem.
Try logging into you system from one of the vtys. Type Ctrl-Alt-Fn to move to a vty.
If you can login from there, then this may be a kdm or the desktops problem. if you cannot login from there, then its a password problem, so from the same vty login as root and change the password.

Have you installed KDE? Try with another window manager...

Instead of using kdm to login, try startx from the command.

Login as root, and fix your passwd.