Because your video card is old, it could be that the newer driversets don't support your card or the game as well. With my old ti4200 for example, I found that my 3D games ran a lot faster with the drivers which were in circulation around the time of my card, rather than the latest ones. In addition, newer nvidia drivers have issues with anti aliasing in Grim Fandango as far as I can tell, causing strange graphical artifacts to appear. This never happened back in the day with my older nvidia cards and drivers.
But Naomi does also have a point. The demo does have outdated code in comparison to the final game, as well as lacking the patch which fixed a number of issues. Since the game is so cheap these days you may as well at least give the full game a try before you do anything more drastic. If the problem still occurs, then you might want to consider rolling back to some older nvidia drivers which are tailored more specifically for your card. Nvidia do great backwards compatability, but it comes at a performance cost as newer and newer drivers are released.
And finally, be sure to tweak around with the various video options in the Grim Fandango options menu. Specifically, try turning hardware acceleration on and off and see if it helps at all. It's a long shot, but you never know.