My ATI Radeon has given me a lot of trouble. ATI doesn't even support it's mobility chipsets (go here (
http://www.ati.com/support/driver.html). For the ATI Mobility Linux drivers, you are redirected to your laptop's manufacturer. So getting the drivers really depends on whether HP supports it.
Personally, I've found great difficulty getting my ATI card to work on both my RH9 and Fedora Core 1 systems. It's supposed to be easy: go to the driver website , download and install. But complications occur and I ended up with a 2D-no-3D-acceleration system. So wasteful of wonderful hardware acceleration =(
So my advice is, don't lose all your hair over this. If you find no success after 10-15 minutes, it may be a good idea to move on and achieve something more worthwhile. Because you are newbie, I recommend using vmware in Windows and installing Mandrake (virtually) on vmware. Then if you have problems, getting back to Windows is as easy as a hot-key or a mouse-click. This'll also smooth your transition to Linux.
Good luck.