Do not trust Geek Squad--they are for the very most part underqualified and clueless, and tend to do more harm than good in many cases (a quick google will reveal many complaints and horror stories).
Anyhow, it shounds like a video problem--could be as simple as a bad resolution setting. In order to find out for sure though, you can provide us with some information:
Go to C:\Program Files\Stardock\Totalgaming\GalCiv2 in windows explorer, or wherever you installed GC2 to if you chose a different location. In that folder there should be a file named debug.err. Just open it up in notepad, select everything and copy/paste it into a post here.