The 6800 might be a couple generations old, but it's a good, solid card that will work well with most games. And it's not that old - only a few years.
It could be a couple of different things. First possibility is that the game doesn't like the versions of the nVidia driver you've used so far. Try switching it with a previous version or with a newer version. If you have the most current version available from the nVidia site, you can also look for leaked drivers.
LaptopVideo2Go has a large collection of leaked drivers that I use. The drivers there are not just for laptop video chipset, but are applicable to all nvidia products - the site simply provides modifications to support otherwise unsupported laptop chipsets. Be sure to try the original nVidia drivers if you've only used drivers from the video board manufacturer so far.
The second possibility (and what my guess would be) is that your video card is overheating, causing the artifacts you see. If you've overclocked your video card, undo it. Check to see how warm your computer gets - try running the game with the case off to see if that eliminates the problem.
The third possibilty is that you have some weird software conflict. I don't know how you'd go about tracking it down, so a full OS wipe and reinstall would probably be the best way to check.
The fourth possibility is that your card is simply dying - there isn't a lot to be done with that apart from trying to get it taken care of under warranty.