since i didn't see this option mentioned and it worked for me, so i'll list it here since i was recently having this issue myself (GTA SA stays cool what can i say
kill itype.exe (intellipoint) in task manager (if you have a MS mouse and/or keyboard you'll most likely have this running)
Am running it as steamgame and the original shortcut has no option to choose compatibility mode, so might be different for hard copies but worked like a charm for me
it can occasionally still get bugged when reloading a saved game or after having tabbed out and back into the game.
enjoy