I've run into this multiple times with laptops at the university that I worked for. The problem wasn't an uncontrolled VGA, HDCP or any of that. Christopher Dean had it right in my situation. The video card simply could not display on multiple monitors simultaneously. The biggest problem for these situations is video embedded into powerpoint presentations. When the video slide would come up, you could see the border, and text, but there would be a black spot where the video should be, but only on one source.
The correction to this is one of two things. Either you can set your Primary monitor to be the Projector, which will then display the video being played, but only on the projector. If in a powerpoint presentation, if the video is not fullscreen, you will still have full view of everything else, but there will be a black box where the video should be. (this was the option I had to use more often than not, as the laptop display was a reference for the presenter.) Or you can simply set the display to projector only, in which case the video should display fine.
If neither of these situations work...you have yourself an entirely different problem.
Let us know how it works out for you next time. I'm curious to know how this is solved.
tl