Sounds like a blown capacitor (or several) on the TV's power supply. I have had this happen to one TV and two computer monitors. I was able to identify and replace the capacitors, but had to use a soldering gun (not iron) because of the high-temp solder that was used.
In the case of my TV, the failure to power on came on gradually, over several months. Sometimes it would power on right away, eventually I would have to hit the power button dozens of time for it to work. Capacitors had bulging tops/leaks when I took it apart. I made sure to use Japanese made replacement caps, not Chinese made ones and it has been working great since the repair (3+years ago).