Your problem is most likely that in the settings for the different displays, the tv is set as a secondary display and the monitor as the primary display. You can set the tv to primary and the monitor to secondary to play the movie on just the tv and have a black screen on the monitor or set them both to primary to have the video play on both screens.
That's the way it is with my Radeon 8500LE. Hope this helps.
for me, I just got a GeForce4 type of card, I got it set up so when I start playing a video (it doesn't matter which player I use) it'll automactly set the size to full size on my TV and I also have overlay on... worked for me but I don't know if you could set it that way on yours, if you could it would be under Settings>Advanced>Your Video Card>Overlay Controls>Check Track overlay rotation, under Full Screen Device choose Enable.... but once again, I don't really know if you could do that with that card (don't know, if you use the same drives as the new ones, I guess you could)