Hi Bus,
I've been playing with video playback from my Thinkpad to my TV recently, so my experience may be relevant... Is your projector connected to a standard VGA connector on the back of the laptop, or via S-video (a small round plug)? On my Thinkpad, the output from the VGA connector is just a duplicate of what you see on the screen, but the S-video output actually comes from a second (possibly virtual) graphics card. From the "display properties" dialog, I have to enable the TV as a second monitor, and can then move windows back and forth between the computer screen and the TV. Something to look into, perhaps.
The reason I suspect something along these lines is this - when you play back video on a modern graphics card, the video picture isn't technically part of the main windows desktop - it's overlaid by some other part of the electronic wizardry. For example, on my laptop, if I play a DVD in a window (ie not full-screen) and try to grab a screen-shot, all I get is a blank rectangle. Similarly, if I pause the DVD and the move the window, I get some very strange effects.
Your problem sounds like the video is possibly being overlaid onto one or other of your outputs, but not both.
On the other hand, I could be completely wrong...
Crispy.