Grounding would be my first suspect. Unless you happen to have a 2-wire jack, grounding is accomplished by the 3 bolts through the mounting plate to the frame. The serrated washers bite into the jack's metal. Remove the bolts and clean all mating surfaces around/at the bolts with emery cloth or sandpaper and re-install and tighten the bolts. Every time the jack is raised and lowered to hook the TT to a TV, there is fore/aft movement in the jack which can loosen the bolts leading to a bad connection.
See if there is an inline fuse or circuit breaker in the positive wire close to the jack. Ours has a breaker mounted to the underside of the head and is easy to miss because it is encapsulated and black. You don't want to cut the encapsulation off the breaker if you can avoid it and would be the last thing I would check. You *might* be able to open up the motor on the jack to expose the wiring connections and verify power is at the motor.
The wiring in the A-frame area is subject to corrosion plus sometimes the wiring is poorly done to start with. You might try checking the connection(s) there.
The jack on our TT failed in about a week from brand new and the dealer had to install a new one. Doesn't have to be a really old jack to fail.