🚀 go-pugleaf

Since you can get the set working by hitting it, I would suspect
either a bad fuse, or cracked solder joint.  Check the continuity 
on all internal fuses (if there are any).  You'll have to test
them since they won't look blown.  

Cracked solder joints can be a pain to find.  Start looking around 
connector pins that are soldered through the PC board.  These 
solder joints take a lot of stress.  The crack is real hard to 
see (It looks like a circle and runs around the pin).  Sometimes 
the easiest way to find a cracked solder joint  is to apply power 
and use a NON-CONDUCTIVE tool to wiggle wires, connectors, and 
components.  If you do that, PLEASE DON'T ELECTROCUTE YOURSELF.  
Remember that there are lots of lethal current sources inside of a TV.