You can check if you're using mirrored or extended desktop mode in the Displays pane of the System Preferences. It would be very helpful to know for sure.
If you're using extended desktop mode, you can try dragging the DVD Player window from your LCD MacBook screen to the TV screen.
Edit: Just saw your post. If you have a menubar on your MacBook and no menubar on the TV, then you're using extended desktop mode. In this case, it's as simple as dragging the DVD Player window off the side (or the top or bottom, depending on how you have you displays configured in the Displays pane of the System Preferences) of the MacBook's LCD screen and onto the TV screen, then putting the video in full-screen mode.