Hello
The probe is with its power supply baord. It gets overloaded or have a loose sodering joint in it that causes this proble. As you know, there is no on sentence answer to any electronic device defects, as they are composed of thousands of components together, each and every component have its own function when we switch ON the set. Just check for any loose soldeigs to this power supply baord, or have some defective components, like bulged capacitors. I hereby attaches the picture of the power supply baord to your TV. Along with attaches an other picture too, not related to your RCA TV, just to give you an idea about what a bulged capacitor will look like. Check these and inform me by Fixya. I'm happy to assist you.
This is the picture of the power board to your TV.
This is the picture of an other TV power supply, which has bulged capacitros in it. Just see the bulged capacitors, red arrow marked. You can see a good one at top right side of the board. OK.