you did type 330 'K' ohm, is that a typo? that resistor is a 330 ohm.

not that that would cause the pop to lock on.

check the cap C20 isn't shorted.

next would be checking the transistor in U3.

instead of me retyping it, it is here:https://www.pinwiki.com/wiki/index.php?title=Bally/Stern#How_the_Solenoid_Driver_Works

whilst it doesn't explain in specifics how to test, you may pick up on where to check?

if reading this you don't quite get it, then i'll try and make it easy for you to test with a multi meter.

with the game off you can try: https://pinside.com/pinball/forum/topic/ca3081-pinout-drive-transistor-number-table

not 100% on game play rules, but have you looked/read part C. on Drop Target & Top Button Feature in the manual.

i'd be concerned about where the power comes in, the 2 yellow wires.

it' looks like maybe the coil has locked on, causing the black shield insulation to melt and short.

i'd also be checking the resistance of that coil, with the burn mark, and that the plunger can move freely as the coil sleeve may have distorted from the heat?