Don't know very much about ATI, other than it never really liked to work with FF7PC. Nvidia is more do'able with FF7PC.
Anyway, if Software mode isn't working for you.... (which means, straight after a standard install of the game. no patches) Then about the only thing you can try are older video drivers. Other than that....I can't think of anything other than switch sides to Nvidia.
About the only other thing you can do is get the PS1 version of FF7. Study up on a program called ePSXe....and play the game that way.