Donah,
I experienced the same thing. In my case I had bad memory. If you are getting blue screens I would check your memory. GC III is memory intensive and its finding the 'bad' areas on your memory modules it sounds like. Gal Civ will NOT cause blue screens. Hardware does.
Two things...
Get 'Who Crashed' a free program that helps identify crash logs..
Get memtest86+ (its free I think) and run it. You have to burn it as an ISO to a disc and then tell your computer to run it when you boot up. This will run a program which will take about 6 to 10 hours and stress your memory and find out if anyone is bad.
Or..
You can just borrow some memory plug it in and see if that works.....
This is my experience and your problem may be different.