It sounds like you have not configured your graphics card. The Mandriva installer seems to miss doing this automatically sometimes, which is why the instructions in the magazine specifically mention checking this.
You can run the configuration tool from the command line after logging in as root. I can't remember the exact name, but type xf followed by tab, or maybe it's XF followed by tab, so find it. Once you have set up your graphics, it should boot into the desktop next time.
"Insanity: doing the same thing over and over again and expecting different results." (Albert Einstein)