Since the TV runs for a bit b4 it turns off, I think you can eliminate BLOWN components. It is more likely and overheating problem causing a shutdown. Without burning yourself, see if you can find a somewhat HOT part. Power devices on a TCON board are typical failure points. The problem is finding it since it works for a while. You can use a DVM and measure base to emitter/collector or gate to drain/source on the power devices. Any shorted devices would probably cause an immediate shutdown so look for open devices which would cause the other devices to run hotter. Otherwise, it is a crap shoot - and you just replace the TCON and hope that is it.