Statistics are such that your problem is almost certainly due to capacitor leakage. If you look very carefully at the logic board, I am willing to wager that you will see some residue.

By all means, reseat/replace ram, wiggle connectors, sacrifice a chicken, etc. Those are easy things to do, so there's no reason not to try them. But if, as is unfortunately likely, those actions don't bring joy, clean the logic board and then replace the caps.