This looks like your first stab at linux, and your first post, So welcome to the board.
The blank screen, it is a command prompt shows up if the xserver ( this server runs the graphical interface ) did not start, is not installed, or is not configured correctly for your hardware.
To try and start it, after a log in as a user or root, the command is 'startx' ( without the quotes ).
During the install near the end, before you re-boot, there is a Summary screen that appears, and down the right side are Configure buttons. There is one there for the xserver. Did you configure it there? This allows you to pick things like screen resolution, monitor type etc. These things are going to be specific to your hardware.
You should be able to log in as a user as well as root. You can create users ( the minimum you should create is one, for each person who will use the system ). Root is very powerful, and should only be used with care for doing system tasks, not running the system. There are screens for creating the users during the install.
So try to startx and see what happens. If you get the GUI going, then go to MCC ( Mandriva COntrol Center ) and set the xserver to start on boot.
Here is a useful link that shows you how to install, it shows the screens I have talked about.
Hope this helps.