Update your video drivers - there are some form last month.
Try running in windowed mode at a smaller resolution. You may be trying to run at too large a resolution that does not support 32bit. The game requires 32 bit.
If you cannot do the resolution in game,, go to your My Documents\My Games\GalCiv2 folder and edit the prefs.ini.
[Video]
DisplayWidth=1152
DisplayHeight=864
ColorDepth=32
Fullscreen=0
Set the dispaly to soething like above or smaller. Minimum Width is 1024, minimum height is 768. Make sure Color depth is 32. Set fullscreen= 0 to force Windowed mode. This mode uses a different XP memory model and is less likely to have issues than full Screen. Once you get it working you cna try fullscreen.
Also, you may want to disable the intro movie to start with - after you get the game running you can turn it on to see it. In the file set
SkipIntro=1.
Hope this helps!