If the Ext.Casing isn't the last piece you built, then you could try exiting the Spaceship-building screen using Escape rather than clicking on the 'X'?
(I have found that clicking the 'X' during the end-game screens can sometimes cause CivIII to crash on my machine, but using Escape or Enter instead works more reliably to move me through those screens all the way to the Hall of Fame)
If the crash happens when you hit the 'Launch' button, then it might be that your computer is having difficulty playing the Space-Race victory-movie.
To fix that, I have seen the advice to try renaming the movie-files in the folder
../[Civilization III]/Art/Movies: after renaming 'Race.bik' to 'Race_OLD.bik' (to avoid deleting it), rename 'Intro.bik' to 'Race.bik'. That way, (if it works) the game should play the Intro movie instead of the Space-race movie -- not ideal, but at least it would get you past the crash.
See also
this thread, and the links from it
Good luck