Update your video card drivers. That's the most likely suspect. I've used two nVidia cards and only had problems with the game before I updated the drivers on one of them. The original nVidia drivers had some issues, and not just with Sins.
If you're still having trouble, email support@stardock.com
Alternatively, how much RAM does your computer use before you open Sins? I doubt it would cause the black screen, but that little RAM will probably limit the size of your game quite a bit. You should think about upgrading since DDR2 RAM is really cheap right now (and I'm guessing you don't have DDR3, if your capacity is so low).