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This is really only a possibility if you have a loose solder joint along the buss of black wires winding its way from the power transformer to the headphone jack, then over to terminal 3.
As far as the LED on pin A3 not being lit, the voltage at terminal 5 suggests that there is conduction here, so that is inconsistent (and also points to a loose ground wire).
The most common loose ground wire is where the black wires meet at the headphone jack. It's pretty easy to solder one to the jack and have one that's just loose.
-PB