might I have a bad tv mainboard or power supply board

Shutting down and freezing, I would start by checking for bad electrolytic caps on the PSU board and around the CPU. you'll need an ESR meter. Also check for bad solder joints on the PCBs.

I believe RCA TVs are made by TCL, given that the RCA company doesn't actually exist any more. So even if you buy another brand it could still be made by TCL, given they're one of the world's largest OEMs of TVs.

 

I think that checks if a capacitor just open, short, or just leaky.
https://en.wikipedia.org/wiki/ESR_meter
A standard (DC) milliohmmeter or multimeter cannot be used to measure ESR, because a steady direct current cannot be passed through the capacitor.

You can probably buy an ESR meter for around $50.
https://www.amazon.com/s?k=esr+meter&ref=nb_sb_noss_2

 

Well you could, but it would take time and money. What you describe doesn't sound like a transistor fault, sounds very much like s bad electrolytic cap. From experience transistors either work, or they fail open, or short in various ways. Like if a switching transistor was short in the PSU, it would probably blow fuses.

Do you have a good electronics store near you, or do you have to order components online?