My computer was doing the same thing as Xerophyte's. Upon launch, the initial screen comes on, goes black, back to desktop for a few seconds, then black for a few more, then back to desktop where it stays. All the while, the CD spins. The disk spins for about a minute after returning to desktop the last time.
This was occurring with all versions of Civ3, including "Vanilla", PTW, and C3C.
I have Window's XP. My problem started a week ago when I installed the latest Microsoft Service Pack. Prior to installing the service pack, Civ worked fine.
I just now was able to get Civ to work. It was a video driver problem. I got the driver from Microsoft through their support websites. There was no new driver from the computer manufacturer website (HP).
So my suggestion is to make certain that your video drivers are up
to date, not only from your video card manufacturer, but also from Microsoft, assuming you are running on their platform.