Hm. An old video card shouldn't be a problem. Mudbox relies much more on the processor than the graphics card to show the mesh. It just turned out for me that the drivers were screwing up the GUI.
Perhaps there's something wrong with your file itself? Did you import it from somewhere else as an OBJ or BIO? If you did, you might want to try creating a whole new object from within Mudbox. From the toolbar, go to Create>Mesh>Basic Head and screw around with that.
Also, does it still mess up after you subdivide your mesh? Or create a new layer? What happens when you change the material? How much did you play around with the settings? So yeah, none of these are a fix, are just ideas for you to experiment with to find the extent of this bug.
I'm surprised that no one else has spoken up. This sounds like a major error, and should have been encountered before.