Because of your determination and persistence (repeatedly turning the set on to watch a program), we will assume there is no smoke or odors coming from the set. Suspect the VCR is not going into a full unload position. To protect itself, it shuts down. If gears have not slipper (the result of forcing a tape in or pulling a tape out), try replacing the VCR's rubber. Don't skimp. All the VCR belts are the same age. Older belts will stretch, get hard or become soft and spongy. Replace ALL the load belts, drive belt, and the rubber idler tire (if present). Suppliers will offer a service kit with all the rubber. If you attempt this, be cautious. Use a permanent marker and mark meshing gears. Many gear sets have markings on them; but may lineup when the mechanism is in a load position.
Mike Andersen, October 2005