The first item and the 4th item are the same thing. Likely, it's either been bashed to pieces because it was too close to the balls, or a bad cable between the sensor and driver board.
Switch #76 is the opto at the bottom of the Mini PF - likely a cut or disconnected wire.
Switch #88 is, well, the only physical switch up at the lock. Likely broken or disconnected wire.
'Rocket Kickout' .. bad coil wire? bad switch? What's wrong with it?
For the sound - board is likely needed a cap kit, or the LM1875 is fried or overheating. Either way, you need board work done there.
Could be anything. Likely disconnected wire. Could be as bad as a fried driver transistor on the Fliptronics board.

Sample games had the 8-driver board like that, instead of upper right. So, @op has a sample game, at least.

There's a hacked ROM version - or mislabeled - in there. There was never a '9.5H' released. (After someone pissed Ted off by hacking 9.4H, he stopped planning on 9.5H.) Someone changed something in that ROM and named it 9.5H. (Never even heard someone reference that version before..)

And yeah, the large cap looks to be connect up to the 5V rail. Interesting.

That's not the end issue.
These proximity sensors use induction. Since the wires that connect the sensor to the driver are not twisted, they can pick up a lot of noise. two headers in the way adds to the noise being picked up, and shifting plugs (from vibration) and wires in said plugs will cause the driver board to pick up variances in induction enough to possibly activate the switch.

I, too, recommend not only direct-soldering the wires, but twisting them as well, to prevent cross-talk and interference.

This system is the same that's used on traffic control loops (speed sensors, occupancy sensors, traffic signals, and my experience - railroad grade crossing occupancy. Inductance works wonders - when everything is set up properly. Change something (salt on the road, for example!) and you get false readings.