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Welcome fellow expert.
This sounds very much like the Inverter board is failing. The board that supplies voltage to the back lights inside the display screen... You may be able to find the board on eBay for less than $100. I can check on that if you plan on DIY, let me know.
There are a few different Power/Inverter boards for this model, so you have to take the back off the tv and verify yours before you replace it.
You cannot test the high voltage output of the inverter board unless you have a 10kv meter.
Two possible board part numbers:
Search eBay for boards.
Or you can get "repair kit" with components to solder onto the boards for a lot less.
go for it. let me know how it goes.
When the picture goes out and sound continues, are the back lights still on (tv screen glows in a dark room), or not?
If not, then try this $27 power/inverter repair kit:
If that doesn't solve the issue then the back lights inside the display screen are bad and you are done because those cannot be replaced.
If the screen continues to glow while picture blinks out, then it is a sign of a TCON board issue.
Then actually may be the low voltage line from power board to tcon board is dropping (may be bad caps on the power board check for bulging tops on caps). Or rather a defective Tcon board (no trouble shooting for that, just replace board).
tcon may be under a thin metal shield. either along top edge of screen or botton edge. has one ribbon cable coming from Main board (board with audio/video jacks).
ok let me know