Hi,
I had a similar fault with a tv and found a simple repair was to locate the fan grill at the back of tv and check if fan is spinning when tv turned on. With a hoover pipe on suction put it as close as possible to/touching the grill and suck for a couple of minutes to get dust out of fan blades and get it working again. I put a tiny screwdriver in the grill and spun the blades a couple f turns and hoovered again and it worked perfectly. Fan chokes and overheats stopping tv from turning on. Might fix it so worth a try.
Good luck
Graham.
PS under sale of goods act 2015 you do not have to prove a fault rather the company has to prove it.