Thanks for reposting here @sinus.

Can you go into more details about the switch issues you are having?
Are some switches not responding?
Are some switches activating other switches within the switch matrix?

What happens if you connect the anode leg of a spare 1N4148 diode to the anode of CR43 and measure the floating unconnected cathode leg? Do you get the same reading on your oscilloscope?

Can you post some clear high resolution pictures of your MPU board so we can see how much battery corrosion it suffered?

The capacitive effect you're getting might be normal. See the second picture on this post:

https://pinside.com/pinball/forum/topic/flash-gordon-target-causes-tilt#post-3220692

It sounds like you might still have some resistive corrosion on the MPU board to deal with. It can get underneath the dip switches which can be difficult to see. The dip switches are also a part of the switch matrix.
So use your multi-meter to check it. The resistance of all the switch strobe lines and switch return lines at the J2 pin header should measure about 57k ohms with respect to ground. If you get any resistance readings that are much lower then this is likely your problem.

Those PIAs are indeed remarks from China. I've used a number of them without issue.

Also, the low resistance readings at the adjacent signals I3 and I4 indicate they are shorted to each other, infact all those resistance readings besides ST0 are too low. It looks to me like you may have resistive corrosion under the pin headers at J2 and J3. It doesn't look like there's any corrosion under the dip switches.

If you measure the resistance across the I3 and I4 signals at the J2 header which is pins 11 and 12, you should measure about 114k ohms. All the adjacent pin signals should measure around 114k ohms across them.

U12 also has bad corrosion - when you get some time remove and clean up that area.

PowerPlay_MPU_J2_CorrosionA.jpg
PowerPlay_MPU_U12_CorrosionA.jpg

Those are excellent readings now
Good luck when you plug the MPU board back into the machine and let us know how it goes.

Which lights went on? Was it just the general illumination lamps or also the feature lamps? If the feature lamps came on, were any flashing? Were they all stuck on or just some of them?

Does the LED on the MPU board flash seven times on power up to indicate the MPU board has passed self diagnostics?

If all the switch strobe signals show exactly the same waveforms then it's indicating that game execution is getting caught in a tight loop.

Sounds a little like you may have an interrupt problem possibly the display interrupt generator is running too fast.
What frequency do you measure for the display generator at pin 40 of U11? Should be around 320Hz
What frequency do you measure for the zero crossing detector at pin 18 of U10? Should be around 100Hz

The switch strobe signals (U10 PA0-PA7) are also used to address lamps and the displays. What happens if you disconnect J4 from the lamp driver board to isolate it from the U10 PAx signals?

Have you re-terminated the wire connectors that plug onto the MPU board?

Great to hear - the display interrupt generator (U12) was suspicious of causing that lockup issue.
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Glad to see you are diving in and learning