my 57 inch zenith doesn't turn on. it will show that it has power for fifteen seconds or so then shuts off.

Answer 1

That could be a power supply problem, a short some place or even failure in the horizontal out put circuit. Most modern TV's have dynamic circuit protection that will shut them off if the current starts to go too high. We use to have fuses and then circuit breakers that would "kick out" if a problem was found, but power supplies are far more sophisticated today.