I’ve had the same problems in a Samsung TV.
On yours, even without a schematic (which is the first thing to look for), it lists the outputs for pins on the connector. And I assume if your going to change a cap, you have a meter. So start there. The outputs at the pins list at 13.2V (it looks like that, confirm in real life). So check those voltages. Then you might be able to just trace back which caps are in the 13.2V output. There will also be standby voltage of a few volts somewhere that runs the logic board.
WARNING: Obviously the TV will need to be plugged in as you measure that. And poking around an open plugged in TV can kill you. Even the new LED TVs with the lower voltage have mains current coming in. Respect that or get bit by it.