Since you are using a Radeon card, you won't be able to run the game in 32 bit color mode.. reduce it to 16 bit desktop color...
if that doesn't help, get the catalist 2.6 drivers.. those work well with SFC.
if you want problem free running og games on PC without having to play match maker with drivers to games, get rid of the ATI and get the GeForce FX 5900 Ultra with 128MB DDR onboard.. Crystal gaming there and all the drivers are WHQL to work.
Radeon has driver problems between games.. such as I have a friend that needs 5 different drivers to play 12 different games....
however, i have always run NVidia GeForce cards and never had a driver problem so long as I only got the WHQL drivers.. on the FX card, all the drivers are WHQL, so no worries there.. And with SFC III - Geforce will run it in 32 bit color, Radeon can't, unless they improved their drivers since last march.
I bet that the problem is your Graphics driver... the Catalist 2.6 I know will work for SFC III, maybe not any other game, but it will with SFC III, however, you will still have to run the game in 16 bit color..
Hope that this info helps.