connector 2J13 is the special solenoid switch inputs, 2J12 is the special solenoid drives.

the pre driver Q9 (2N4401) may be faulty?

can you check pins 4,5 & 6 on the 7402 IC9?
both inputs, pins 4 & 5, must be low for the output pin 6 to be high.
if both of the inputs are low the problem may be IC6 seeing as you have changed IC's 7,8 &9.

yeh my bad, was looking at an original schematic, not taking into account a different driver board.

so when you tested the pins, I assume the coil wasn't locked on?

also forgetting that you would need to desolder a wire from the sling coil when doing the test, need to test the NOR gate when the coil is on.
if the coil was on and you got those same readings it looks like IC6 to me.

your results show off, but it does look like you can use your logic probe.

to completely isolate the switches you could remove a wire?
the coil energising and subsequent scoring is the other switch that closes when the 'arm' moves.
there are the 2 switches through the playfield that energise the coil and one that closes which is part of the switch matrix that causes the scoring.

i'm wondering what you can put in place of the solenoid so as to do testing and not cook it......maybe 2 x 24V car/globes in series, this way when it's on you will see the globes light up?