I guess it's finding your DVD OK, otherwise you would get the "Please insert the original disc" message. Does the same thing happen if you try to run Play The World?
Try holding down the Option key while you launch it, to get the Display Preferences dialog up. If that appears, check the settings. Maybe something there has become corrupt.
Next option - try trashing the Preferences file. It's at:
<Home>/Library/Preferences/com.aspyr.civ3conquests.plist
If that doesn't help, try trashing the .ini file:
/Users/alan/Library/Preferences/Civilization 3 Complete/conquests.ini
You could try reinstalling Civ - maybe something in the software is corrupted.
Have you contacted
Aspyr Support?
Is anything written to your system or console log when this happens?
You can open the logs by launching /Applications/Utilities/Console and then selecting 'Open System Log' and 'Open Console Log' in the File menu. There may also be something in the CrashLog for Civ3.