The problem I was having was that after completing the Endor mission in the Galactic Conquest, the game would exit to desktop.
I did a little searching around and it appeared that the registry key was missing from my registry. No idea why it was missing, but it was none the less.
I didn't uninstall the game since I didn't see an uninstall under "Add/Remove Programs".
I put in disk 1 (the play/install CD) and when the autoplay brought up the menu to install the game. After starting the install... it barreled through the first bit and then popped up asking for disk 3. I put that in, and then it asked for disk 1 again. I put that in, and finished up the install.
Once that was done, I confirmed that the registry key was actually in the registry, and also confirmed that the "Add/Remove Programs" also contained an entry for "Star Wars Battlefront". Since both things looked okay, I ran the game.
I loaded up the Galactic Conquest game where I was stuck at Endor. I completed the map with a victory (for the Nth time. Low and behold... No crash to desktop. It played out an animation and things appear to be fixed.
I hope those of you having similar problems find this info to be helpful.