The video card doesn't really matter when rendering, that's only for the viewport. Mental ray, or the Software renderer are pure-cpu related activities.
If you're using Mental ray, change the quality preset to Production, same goes with software; and those edges should be dealt with. Another thing you might want to look at, is if one of your texture maps is causing it. Something like a displacement map, or bump map. Try assigning just a normal default lambert to the object, and see if it renders properly.
Imagination is more important than knowledge.