I initially thought it was a bias problem. After seeing the scope image, it seemed to be more of a power supply problem. I've seen muting circuits distort the signal so that was one of the things to check when you stated that all of the supply voltage were OK.
The opto-coupler switches the power supply for the differential amplifiers. This isn't a conventional muting circuit where the audio is clamped to ground. It disables the first stage of the amplifier.
If shorting pins 3 and 4 of the opto-coupler makes the amp work properly, the problem is that the opto-coupler isn't being driven fully on. The capacitor on the base of the transistors that drive the LED for the opto-coupler has been leaky in other amps and when leaky doesn't allow the opto-coupler to be driven on fully.
Thanks. Got it! I've never gave-up to this <$50 cheap amp, even I've spent a lot of manpower. Amp owner still hoping for his amp 🙂 to get it work.