With memtest86+, download the iso, burn it to a disc or flash drive and when you boot it will automatically run.
It's a looping program of several tests. It will run indefinitely until you end it. One or two passes isn't enough to guareentee the RAMS fine so that's why I suggest letting it run over night while you sleep.
If theRAM passes, it will show zero errors. If it fails it will show how many errors. You're aiming for zero.
I only suggest downclocking the card as a test. If it runs fine while downclocked then you know the cards a dud and needs to be replaced. Downclocking is quick and not permanent.
It may also be worthwhile downloading and installing the latest physx package (even though ATI doesn't use it)
NVIDIA PhysX System Software
However the fact that GTA IV and AC ran fine tends to suggest a software issue rather than a h/w one.