3GS turns on only when powered by cable

I have a 3GS restored after mechanical damage, it appears to be functional but one problem persists: I can't turn it on with the power button when it operates from the battery. It has to be plugged into a charger/PC to start functioning. After it's on, the charger is no longer needed, it can keep operating till the battery runs dry. The button is fully functional when the phone is already running or when it's in standby mode but powered by cable.

The circuit of the button appears intact, oscilloscope indicates 350mV on the contacts when it's pressed and 4.2V when released, seems like the button itself is OK and the pull-up resistor feels fine as well.

What could it be and what else can I check? I suppose the power controller (338S0868) is dead.

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