Thank you for the suggestion.
I think I understand what happened.
KeepRes is already =1. I am using screen resolution 1280x720. If I switch to 1024x768, then Civ3 starts fine, but does not fill the whole width of the screen. If I set KeepRes =0, then I can start the game at any resolution, but it will switch to 1024x768.
Now, I vagualy remember, that Civ3 wouldn't run at 1280x720, perhaps because it needs at least 768 vertikal resolution. That wasn't a problem, because I used 1366x768 as default screen resolution. But then Microsoft stepped in and with an update subversively removed that resolution. So I am now using 1280x720 or 1600x900 in stead. At 1600x900 Civ3 runs fine, but windows (like the city screen) are smaller due to being only 768 pixels high.
1366x768 seems to be the best resolution for Civ3. Hail Microsoft!