Sometimes the video memory gets overloaded and you have to flush it... 1. Press Shift and - (minus key on the KEYPAD). 2. Type FLUSH (you won't see the letters) You should get a message and the video buffer will flush. If this persists - make sure that the video memory in the options is set to DEFAULT.
Still doesn't work. Set the video memory to default, loaded up the mission, black screen. Did the flush, and it said flush activated, little loading screen, black screen again. Tried setting the graphics settings all to low, still black screen. Works fine if I go into Free Flight. I'll try going back to the previous career mission, see if that works.