I am told that ringed planets are drawn fine on Radeon 9500 or higher.
Apparently there have been bugs for a long time in ATI's OpenGL drivers for Radeon cards with model numbers less than 9500, and they don't seem to be interested in fixing them
One of the symptoms is that the surfaces of ringed planets have black blotches on them when ring shadows are enabled.
One workaround is just to turn off ring shadows in Celestia's "Render" "View Options..." menu.
Another work-around is to tell Celestia not to try to use the OpenGL vertex routines when you want to look at ringed planets. Type a Control-V until you see "Render Path: Basic" or "Render Path: Multitexture".