My guess is that the screen resolution x-plane is set to use is not supported by the tv. if you have another monitor) you can probably get away with starting X-Plane on the other monitor changing x-plane to window mode rather than fullscreen, and then setting the resolution to the same resolution you use for your desktop (windows settings). At any rate when in windowed mode the computer will keep the same resolution your system is already set up and working at.
Just a first guess... Hope you get it sorted out.
Bao