In short, you're probably looking for the wrong file and probably want conquests.ini instead.
There are three flavors of CivIII, original ("vanilla"), Play the World and Conquests. Each executable uses its own .ini file, and the .ini file doesn't exist until that game is run.
Civilization.ini is for the vanilla game and is under the main program folder, by default c:\Program Files\Firaxis\Civilization III . Conquests' .ini is conquests.ini and resides under the Conquests folder under the main folder. Play the World's .ini is ptw.ini and is in the Civ3PTW folder under the main folder.
Here is a <2-minute video I made where I alter the conquests.ini file for some preferred settings including keeping the native desktop resolution:
http://www.youtube.com/watch?v=fPAh8s0Nqzk . The main CivIII folder is in a non-standard place because that's my way to solve some problems with running the game under Vista, Win7 and Win8, but the subfolders are in the same relative position to the main folder.
If you still can't find the file you may be running Vista, Win7 or Win8 and running into VirtualStore which I won't get into now, but if that's the case you may want to uninstall and reinstall into an alternate location as I show in this 8-minute video:
http://www.youtube.com/watch?v=OC7ALkeoZmE