Hi

It does sound like someone disconnected that wire because of the fault you are now experiencing. As you suggest, the reason for the stuck on coil is probably a fault on the driver board. Q12 I would consider is the first place to check as this is the transistor that drives that coil and it sounds like a classic blown up transistor stuck on. Q12 is towards the top left corner of the driver board ie the bottom board. Q12 could have blown because of a faulty (open) diode across that left kicker coil. So replacing that diode was a great start. BTW Did you test the diode? Was it indeed bad? If so, then this is a strong contender to why you may have a blown Q12.

Cheers,
edit : Ohh A dead shorted diode would cause it too and generally a very burnt transistor is what you may see at Q12 in that case