There is a key you can add to the civilization3.ini file in the main directory that forces that game to use whatever your Windows resolution is. If you are running anything 1024x768 or higher, I would think it would allow you to run the game without your video card and monitor switching video modes. Then if the problem goes away, great!
Unfortunately, I can't find the info. I think the option was adding
KeepRes=1
to the civilization3.ini file but I'm not sure cause I saw this at apolyton.net for an unrelated problem but if that uses the same mode as your Windows session than that would elimate the mode switch and perhaps fix your problem. If not, then something else or another driver might be problematic. Back up your .ini file before you try it though, I'm not sure if that was the right option but I saw it I think at the Apolyton "help" forum which I can't access now due to server load.
Jay