I finally figured it out, after a whole day of working in the terminal. In order to make it work properly (on the Ati Radeon Xpress 200 card), you have to do the following steps:
1. Download and install the driver provided by ATI at: http://ati.amd.com/support/driver.html
2. Follow the instructions for your particular Fedora distro at: http://forums.fedoraforum.org/showthread.php?t=189227
3. Open /etc/X11/xorg.conf, and in the Driver section, replace the text "fglrx" with "ati". Save and exit.
4. Reboot your PC.
5. If this does not work the first time, don't fret, i didn't for me either. I had to go back and re-edit my /etc/X11/xorg.conf file (as root), and reboot, so that the changes would take.
If this does not work for you, please let me know, I'll try to help out in any way that I can.
Please note: These steps may have to be repeated each time your kernel is updated, but eventually, this issue will be fixed by the Fedora developers (or the Fedora community), and the driver packages will become fairly simple to deal with. Example: I had the same kind of issues with the old Nvidia drivers in Fedora Core 3, 4, & 5, but by Fedora 7 I could download and install the Nvidia drivers as RPM packages, and they "just worked" without having to edit configuration files and such.