I'd guess your Radeon HD 6950 is on the way out if not your RAM. It's also possible you've overclocked the 6950 too much putting unnessary strain (and heat) on it. Run the game with it back on factory settings and/or try running the game on High rather than Max settings (i'm assuming you are on max). Your processer is aging but should be fine...

If you want a comparison, I'm running this game on a first gen i7 920 processor (it's now obsolete), Raedon HD 5670 (old for Radeon cards), and 16 GB RAM without issues on High settings. I was able to benchmark decent scores on max settings, but it's not feasible for live.