I've just recently bought Civ4 Complete (without trying the demo...), and am new to Crossover (and Steam, by extension).
I was able to install Steam without any problems, and dl'ed each version of Civ4 without problems. I can start each version of the game, but the window will close itself anywhere from the leader select screen up to the first couple of turns of play. However, the icon for Civ will still be on the Dock, and I have to quit on my own. Since the game isn't quitting, I'm not getting anything in the PythonError log. The same thing is happening for each version. This may or may not tell you much, but I'm having the leaderhead graphical glitch, as well as getting a tower of fiber-like things where the units should be, if I even make it that far.
This issue has been forwarded to the Official CodeWeaver's Ticket System. If you have observed this issue and would like to report it as well, please open a support ticket or send an email to info@codeweavers.com with a description of what you are seeing and a link to this post.
Thank you!
The CodeWeavers Team