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Repair melted wall connector.

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I'd guess the circuit board just connects the DC power supply to the input mains through those small black wires. I'd expect the actual high amperage connection to be directly connected with the terminal block and not through the circuit board. I'd probably try to source an entire replacement board or failing that replace the terminal block.
 
Did you fix this? I'm curious, because I just replaced mine with a JuiceBox that my power company provided for a $31/mo unlimited off-peak hours plan and mine was melted at the green 2-position terminal block (although still functional when I disconnected it with new errors/problems).