I had the very same problem.
Here is Stardock's response. It worked on my system.
Try going to Documents\My Games\GC2TwilightArnor and open Prefs.ini.
Change DisplayWidth and DisplayHeight to whatever your screen resolution is, save the file, and then try again. If that doesn't work, set Fullscreen=0
You can also do this at Documents\My Games\GC2DarkAvatar and Documents\My Games\Galciv2
If this doesn't help, please go to Start->Run and type dxdiag. Once everything loads, please click the "Save all information" button and attach the output file in a return email.
Please let us know if this resolves the issue, or you require further assistance.