Start by checking continuity from the black wire, back to the solenoid board.

It looks like your connectors are original. They may be causing your issue.

You could test for this by checking continuity from the coil to the transistor. In this case, Q12 is for the RT Sling-shot.

The connectors at J4 & J3 are also suspect.

well you have determined the mpu is registering the switch closed in the self test but the signal isn't going the other way, from the mpu to the solenoid driver.

you could have a faulty PIA U11, you could try swapping U11 for U10, if the solenoid fires when the switch is closed then U11 is faulty.

the signals from the mpu go to J4 on the solenoid driver.

the base of the transistor isn't getting turned on, needs to go 'high'.

if you have a logic probe check for a high pulse at the base of the transistor when the switch is closed.

When you 'ground out' the coil where exactly are you grounding? Since only 1 coil is bad and you changed the board I suspect it's a problem with the wire or crimp. Try removing the coil wire from the plug and grounding there.