That bare wire is factory, it's soft and flexible to minimise any effect on the swinging tilt plumb-bob.

It shouldn't be screwed to the slam switch assembly though, it should be screwed to the wood board on its own.

First picture is the generic Bally setup.
Second picture shows someone moved the slam switch close to the tilt plumb-bob in what looks like a similar way to yours with the bare wire screwed to the slam assembly.

TiltBoard.jpg
TiltBoard2.jpg

Maybe a problem with one of the 30 point rebound switches. There are two of them which is switch #29:

MrMrsPacMan_SW29.png
MrMrsPacMan_SW29_locations.png

Once you're on the 2nd ball in play, there's no going back to ball one in the same game. Pressing the start button will cancel the current game and start a new one.
As long as the game is on the 1st ball in play, you can add new players till you have four players.
That's how all early Ballys work.

TiltBoard_capacitor.jpg

Looking at the capacitor won't really tell you anything. It only needs to become very slightly resistive (low mega ohms) in failure causing it to discharge between switch read cycles resulting in the tilt switch to appear closed. And this is a common failure of that capacitor.

You need to disconnect one end of the capacitor to see if the problem goes away.

The capacitor circled in the pictures above is the only one on the tilt switches.
BTW post a better picture of the tilt board face on. I can't see exactly where the capacitor is connected in your picture because its position looks different to my picture.

The coils will not activate so long as the game is tilted.
Try this:
With the machine OFF, disconnect the J2 connector (which is the playfield switch harness) from the MPU board.
Power ON. Does the Tilt lamp come on? When you press the start button does the ball eject to the shooter lane?
With the machine OFF, reconnect J2 but disconnect the J3 connector (which is the cabinet / coin door switch harness) from the MPU board.
Power ON. Does the Tilt lamp come on?

Put the game in lamp test mode (press the little red push button switch inside the coin door once). Does the Tilt lamp flash on and off?

Ok.
@troyster42, remove the J3 connector from the MPU board and briefly jumper MPU J3 pin 1 to ground to simulate the self test button.

The game is not completing the boot process. The MPU board in the backbox has a LED that should flicker the very moment you power-on and then it should flash a number of times indicating certain devices have passed tests. Can you upload a video showing the MPU LED showing just before you power up and after it stops flashing?

PinWiki has the LED flash details indicating what device has just passed tests so you can determine where the failure is occurring - if you want to read up:
https://www.pinwiki.com/wiki/index.php/Bally/Stern#Bally_.2F_Stern_MPU_Board_LED_Flash_Sequence

Can you post a video? The flicker after the 7th flash is odd.

Hmm, it's crashing just as it's about to go into attract mode. After the 7th flash, the LED should go dim indicating program execution is running normally.
You have a MPU board problem here.

May I suggest you open a tech support thread in the early solid state tech sub-forum because discussion from here will have nothing to do with Mr and Mrs Pac-Man. We can follow up there.
https://pinside.com/pinball/forum/forum/tech-early-80s-solid-state