A 32" flat screen and mounting bracket weighs less than 10 lbs. I'd suggest to make a plywood panel to attach the screen's mounting bracket. Depending on the dimensions of your cabinet, an articulating mount may be enough to get the screen inside the cabinet. If not, you may have to hinge or build a slide so the screen slides back into the cabinet.
FWIW, I have a 32" screen that is mounted to a 5/8" plywood piece, using an articulating mount. The plywood is screwed and glued to the Luan paneling and into three studs. I don't do anything except folding the mount close to the wall before traveling. The screen barely moves.