The best thing to do in this case is to not assume that these may be all related problems, and treat them as individual problems, break out a meter and start logically troubleshooting as if you have one coil problem. If they are related, whatever you find is the problem may also be the cause of the others.

Troubleshooting coil problem basics for WPC based games starting point - I recommend reading section "Checking transistors and coils" @ http://techniek.flipperwinkel.nl/wpc/index2.htm#trans

I'd highly suspect a bad trace that would carry the D7 signal, somewhere between the ribbon connector (J113) and the solenoid latches (U2 - U5). It wouldn't be at the ribbon connector itself or it would cause flashers, lamp matrix, etc. to have problems.

Are these all on the same circuit? My buddies did the same thing and it was a wire that had come loose under the playfield and was causing several coils to lose power. Inspect every coil and reflow the solder on them.

One quick test you could do without pulling the board would be to put a DMM on continuity and check between the ribbon header and the pins of the ICs. If it's not obvious, do this with the power OFF.

Assuming the solenoids are failing as consistently as you say, it should be pretty easy to identify an open circuit. If you have mini-grabber clips available, you could also hook onto those locations and do your "pressing on the PCB" test to see if you can get your DMM to beep intermittently.

I see it!!! Nice find and thanks for posting Now it's searchable and will no doubt help others.

That chip has been replaced and someone did a pretty poor job of it. All of those pins could stand to be resoldered. I'm glad it's working, though.

Nothing to be ashamed of. It takes practice, and everyone tells you not to use too much heat, so most newbies don't use enough heat. Your goal is a shiny, smooth curve from the board to the pin.