I'd like to point out this only happens in Galactic Conquest. I'm doing Birth of the Rebellion, went from mission to mission, had no problems, went to Kashyyk, did the battle, I won, the game gave me my little victory screen and stats. Then I hit next. Black screen. Annoyed, but sure this was just a one-time thing, I did the battle again. Afterwards? Black screen. Then again. Black screen. I've now done this battle 6 friggin' times, changing different things both with the game and my computer itself in hopes that it'd work, but it simply doesn't.

Any ideas on what could even be causing it?

Huh. Strangely, I tried it again, having read about someone that just waited a few minutes and went away. I don't think he had the same problem as myself, but I went to try it anyway. I finished the battle and didn't even have to wait. It just continued on normally for me.

With that said, I wouldn't want this to be marked as solved, since, "Well, just do a battle 7 times or a billion times until the game is suitably pleased with your dedication to continuing as to let you progress," isn't exactly helpful to anyone whatsoever. I'm sure that if I've had this problem, others will at some point as well. So, I suppose, leave this thread open for someone to just continue it if they have a problem.