My 8yr old TV was turning off and on about every 20 seconds. The red standby light and backlight were on (as seen in a dark room), but the screen was black. I removed the main (logic) board and locally slowly heated the largest chip (integrated circuit) to about 200C for a few minutes with a hot air gun (see 'reflowing mainboard' videos on youtube). On re-assembly, it all worked again.
After a few years, the solder cracks around chips that get hot ie the big chips often with heatsinks. Re-heating the solder to about melting point reseals those cracks. The job takes about 1hr and requires moderate DIY skills.
Sometimes TV's fail due to faulty bulging capacitors in the power supply board, but mine were fine as were the voltage outputs, so 'reflowing' the solder can be thought of as a last resort. If this job looks too daunting, try taking it to a repair cafe.
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