Even with that CPU, there should be an improvement. I would look at the PSU, as there is a drastic difference in power draw between a 9600GS and a 4870. Performance will suffer if lacking sufficient juice, but not lacking enough to cause a restart.
I've installed the drivers and uninstalled the old ones, and my power supply is rated as 50W above the amount needed to run the card. As far as games go; Dragon Age runs the same, and World in Conflict the demo for crysis run slower.