The schematic states D1 or R16 should be installed. R4 should always be installed.

This game isn't a Bi-Phase switched illumination game.
R4 is currently seeing 43 volts (instead of 21.5 volts it should be) which is causing it to dissipate nearly 4 times the power (well beyond what it's rated at) and that's why it's burning. You need to remove D1 and install R16 (2k ohm resistor). I usually replace both of these 2k resistors with 1/2 watt variants because the 1/4 watt rated resistors in use are running close to their max rating. I have seen them go open circuit from fatigue.

It might be possible that the MPU boards 5V supply rail is seeing high voltage spikes/dips when you activate the flippers because of the excessive voltage at R4 from the solenoid power rail. It's potentially a reason for the resets.

You sure you didn't install any of the capacitor on the sound board backwards?

What state is the female connector in that plugs into the sound board?

What voltages are you measuring at test points TP1, TP2 and TP3 on the sound board?

If you have a logic probe, are you getting activity on the four "SND SEL" and "SOUND INTERRUPT" inputs on the sound board during sound playback?

What's the voltages at test points TP5 and TP1 on the solenoid driver board?

Voltages look ok other than the sound board TP1 fluctuating. If you put your black meter lead on another ground point, do you get a stable voltage reading?

BTW, does the flipper reset happen intermittently or every time you first flip in game mode?
Does it require both left and right flippers to be activated at the same time or only one (either/specific) side?
When it resets does the game play the alarm you hear when you slam tilt the game?

??? Check if this is a mechanical problem by you flexing the MPU board a little around TP5.
Where are you hooking up the logic probe to ground when you're doing this? somewhere in the backbox or the Gnd test point TP4 on the MPU board?
How much voltage do you measure at TP5 on the MPU board when you use a common backbox ground point for the black meter lead vs using TP4 ground on the MPU board?
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How many flashes are you getting on the MPU board LED when the game doesn't boot?

If you disconnect J1, J2 and J3 from the MPU board (leave J4 connected only) does the MPU LED still blink forever?

If you swap the two 6821 chips on the MPU board with each other, does it change anything?

On the sound board are you measuring zero ohms continuity between the negative leg of capacitor C24 and TP3 (Gnd) on the sound board?

On the J1 connector of the sound board, pull out the wires coming from the MPU board one at a time to isolate the connections and see if you can narrow down which signal is causing the boot issue.
Start with the wire at pin 8 on the sound board connector. If no difference then the wire at pin 2, then 1 then 3 and finally 4.

To clarify, unplugging J1 from the MPU board makes the MPU board LED blink 7 times and then the LED goes dim like it should?

With those 5 wires unhooked from the sound board you disconnected all the logic signals from the MPU board to the sound board. That just left the sound board with ground and the unregulated 12V connected.

So it's pointing to a problem with your unregulated 12V supply and a problem here could cause the flipper resets.

Which solenoid driver board (SDB) have you got? Bally factory or some aftermarket SDB?
If factory SDB, is the big capacitor at C23 original?

Can you post some clear high res pictures preferably taken outdoors in shade (so your camera gets maximum natural light without shadows) of this MPU board front and back?

Hmm, I can't see anything abnormal in the pics.

Question: are you hooking up a battery to this MPU board when it's in the machine?

Humor me, please hook up a battery pack with blocking diode.
This board isn't a standard Bally -35 board. The reset section and battery backed RAM rely a little more on a battery being present.

Ok, set your logic probe switches to "TTL" and "Pulse". Hook it up (black lead to ground, red lead to +5V). Do you now get any activity on the four "SND SEL" and "SOUND INTERRUPT" inputs on the sound board during sound test mode?

With your logic probe still hooked up, probe pin 40 (top left pin) of the 6802 CPU. Hold the probe there, it should indicate High. If you tap a flipper button with the other hand a few times, do you notice the yellow "pulse" LED or green Low LED on the logic probe flicker when the game resets?

Yes, and don't forget when you get a NVRAM you require a 5114 compatible replacement, not standard 5101 replacement.

I've gotta bail so will check in later.

If you have a spare 6802 chip, swap it in.

Sorry for the delay.

So something is triggering the reset circuitry on the MPU board.

How much voltage do you measure across zener diode D2 on the MPU board (bottom left corner)? Put your black multi-meter lead on the lower diode leg, red meter lead on the upper diode leg to ready the voltage across the zener.

With your bench testing the MPU board and the LED non stop flashing, is the reset line on the CPU (pin 40) steady high or is it pulsing low every now and then? If it's pulsing, how many LED flashes between the reset line pulsing low?

That's too low. It should be over 7.8 volts and preferably closer to 8.2V which is what that zener diode spec is. I don't think it's your problem, but please change it if you have a spare.

With your logic probe, what's happening on pin 13 of U15 (input to the reset pulse chip) during this never ending LED flashing?

Battery still hooked up to the MPU board? What happens if you pull out the 21C14 memory chip at U6?

Are you counting the initial power on LED flicker as a flash?
Without the battery backed RAM at U6, on power up you should get a quick flicker, flash, pause then 2nd flash and that's it.

With the RAM reinstalled at U6, what voltage do you measure on pin 16 of U15? Does it change after every 3 LED flashes?

For now, if you have a spare 1N4148, 1N4004 or 1N4007 diode, can you put it in series with the D2 zener diode to add an extra 0.6V voltage drop?
i.e. unsolder the banded side of the zener and lift that leg out of the board. Solder a generic diode banded leg to the banded side of the zener. Solder the other leg of the generic diode into the board where the banded leg of the zener originally was. This should lift the voltage across the zener points on the board to around 7.7 volts.

Am wondering if the RAM at U6 is suspect. First, please add a generic diode to the zener and lets see what happens.

Power on the board and then jumper a piece of wire from the lower leg of resistor R24 to pin 18 of the RAM chip at U6. This should stop the reset circuit reactivating.
What happens to the LED flashing?

Can you power the board off then back on with the jumper wire still in place? How many LED flashes do you get?

Timing of the reset circuitry is critical to how the CPU starts up. Since that jumper wire is essentially bypassing the reset delay circuit on powerup, depending on when you power the board and how much the caps on the board were still charged from the last power down, startup will be unpredictable as you just saw (sometimes boot success, sometimes the CPU starts before power has stabilised and crashes).

On this revision MPU board, Bally have added some protection circuit to the battery backed RAM at U6 to prevent data corruption on powerup.
What appears to be happening is on powerup when the CPU begins to test the RAM at U6, the signal to enable the RAM is causing the protection circuit that's powered by the "battery voltage" to crumble and is causing the reset circuit at U15 (also powered by the "battery voltage") to reactivate.

At this point I would remove the RAM at U6, carefully bend pin 18 out and reinstall the chip with pin 18 hanging out. Connect pin 18 to 5V power on the MPU board so it's no longer being powered by the "battery voltage".

Another thing you could temporarily try is disabling the RAM protection circuit. Remove resistors R9 and R10 and short out diode D5.

However I have a feeling the problem may be upstream in the "Valid Power Detector" circuit on the MPU board because your other issues with the flipper resets and hooking up the sound board are more likely to be propagated onto the 12V supply line going onto the MPU board where it's used in the valid power detector circuit. Mind you, you have now corrected the voltage across that zener diode.

The Valid Power Detector circuit on the MPU board shown in the schematics has a few voltages listed at various components. Might be worth checking those voltages..

Please try replacing diode D4 (with a 1N4004), and then disconnect pin 18 of the RAM chip from the +5DC supply you hooked up to and connect pin 18 back to any "battery voltage" (aka VAUX on the schematic) point like the top leg of resistor R3.

The sound board static is likely a separate issue.

Your "unreg 11.9VDC" measured 15.2V at TP2 on the MPU board which is about right when you factor in the large capacitor on the solenoid driver board removing the majority of the DC ripple on that supply rail. So 8.0 volts on the anode of D2 is no surprise and has propagated to other voltages you measured.
If it concerns you and your transformer is still wired for 115VAC, change it to 120VAC (with the power cord disconnected from the wall).

BTW, what's the history of this machine/board? Was it working and then started to fail, or did you buy it with these problems?

Before you replied, I modified my post #35 above to change D4 from a 1N4148 to a 1N4004. Which type diode did you use?