I had an ati 4670 in my old machine, with 4 gigs of ddr3 1600 and a phenomII at 3.2GHz. Was running AH in full HD, hi res tex on, 2048 texture size, anti-aliasing one notch from the top, 2048 shadows, everything else maxed, but the smooth shadows were disabled, with a steady 55-60fps. It only became short with the smooth shadows, 4096 shadow texture size, and later with the ground cutter and the reflections. With my current 5830 (~7770 level), same type of CPU, twice as much system ram, i have everything maxed out but the anti-aliasing (one notch from the top) and the dynamic reflections set to static. It could handle it 2 notches better, but i dont like the way this feature looks that way.
If youre only using your computer to play AH, surf the net, do some daily work, a 7770 or a 650ti might be a good choice for the next 2-3 years. That old C2Duo will be able to handle that. But if youre planning to build a completely new system, then i would buy an at least 7870-7950-660ti-670 level card so your new build might last much longer.