I had a similar issue with my notebook. Oddly enough putting it into software mode fixed the problem, of course there are huge drawbacks to doing that.
Looks to me like a problem with the texture filter. Try playing with bilinear, trilinear, anisotropic to find out if there is a setting in which both computers are the same.
Also you might try to enable "Use custom setting" in the control center of the ati card (enabling that did for some reason sometimes help with texture problems in our game).