Your sidebar indicates that you are using Slackware.
By default, in Slackware, you login to the command line, then issue "startx" to start the GUI. You exit the GUI to the command line, then issue the shutdown command as root ("shutdown now -h") (granted, there are other ways to do it, but this is one). What happens when you do this?
(Of course, you can issue the shutdown command from a terminal as root while still in the GUI. In Linux, there are often many roads to Rome.)
Please provide more information. Are you booting to the command line or are you booting to a graphical interface (runlevel 4)? What make/model computer are you using? What is the output of the command
issued in a terminal?
With enough information, we should be able to figure this out.