From your description it sounds very much like the TV power supply.
I used to repair TV's and other gizmos.
I doubt if you can initiate the menu when the set goes down.
Yes pixelation occurs with weak signal. As in antenna problems
The power supply usually or nearly always has a safety cutout device.
Try running a DVD video. I bet the problem will still be there. That takes the aerial out of the equation.
It may not be just the power supply. It may be another problem triggering the safety cutout from overload.
One for the repair shop or if its a small screen, replacement.
Cheers
