Indeed, the TP5 voltage on the solenoid driver board should be between 14.5V -16.5V DC. The large C23 electrolytic capacitor in the middle of the solenoid driver board is responsible for raising it up from the 11V mark. The capacitor has either failed or lost connection, more likely the latter from a bad connection at the J3 connector.

The low TP5 voltage is resulting in the 5V power for the MPU board being too low (you measured 4.07V at TP1 and normally this should be around 5.2V) and that's why the MPU board isn't booting.

Post some clear high res pictures of the solenoid driver board so we can look at it.

Quench has you on the right track George. Here is further reading on that era Bally: https://www.pinwiki.com/wiki/index.php/Bally/Stern#MPU_boot_issues

The black and orange wires hanging off the board is someones attempt to fix a bad J3 connector by bypassing it.

The black wire actually goes to the negative leg of the big C23 capacitor and I'd suspect it may have had a bad connection in that twist socket.
Before spending any more money on boards that connector should be fixed because one of your other test point (TP3) voltages was a little off again because of that connector.

Now you can actually mask these two connector issues by performing the following "upgrades" on the solenoid driver board and in your position I'd do these before anything else:

https://www.pinwiki.com/wiki/index.php/Bally/Stern#Solenoid_Driver_Upgrades

As Quench says, job 1 should be to replace the J3 connector. Those original IDC type connectors are pretty much one and done so I recommend ordering a new KK style rebuild kit.

Big Daddy's eBay store is back up and you can get a complete solenoid driver kit from him. You can visit his store here: ebay.com link: str

Kits to order:
ebay.com link: itm

And you should replace the original filter caps: ebay.com link: itm

I'm not sold on rebuilding the entire board but I do recommend jumpering J3-25 to pin 13.

Until you get the 5v operational its a good idea to hold off on installing the new MPU.

The solenoid driver boards are pretty reliable once you get them going. That one looks like a fine candidate to fix. Repin that J3 connector, change both main filter caps (C23 filters your 5v and the other silver one to the left filters the display voltage, Id suggest changing both), reflow all header pins (also check solder joints on the 6 pin relay above J2, I find they are commonly on the verge of breaking but not quite broken yet). I suggest removing the old solder with a solder sucker and applying new solder instead of mixing new solder with the old. If you're not strong on soldering practice on a scrap electronics board.

https://www.arcadepartsandrepair.com/store/pinball-kits-parts/pinball-kits/bally-as-2518-22-solenoid-driver-pcb-105c-cap-kit/
You can also get the crimps and connectors from this site, although I dont think they sell a kit there. I think these caps are better quality than what Big Daddy sells

Set your multi-meter to AC voltage.
Put the black meter probe on the negative (left) screw connection of the big blue capacitor in the middle of the solenoid driver board.
Put the red meter probe on the positive (right) screw connection of the big blue capacitor.
How much AC voltage do you read?

Next, move the black meter probe to any ground point leaving the red meter probe on the right screw terminal on the big blue capacitor.
How much AC voltage do you read?

Measurements should be in the 300 millivolts (aka 0.3 volts) range so the tests will give us more insight.

That's abnormally high and doesn't make much sense. Probably time to replace that capacitor.

If you're inclined do these last measurements.
Meter set to 20VDC scale.
Black meter probe on the GND test point on the solenoid driver board (left side of he board) and keep it there.
What voltages do you measure on each screw terminal of the big blue C23 capacitor?

Ok, that says the capacitor is "connected", i.e. it's not malfunctioning because of a bad connector upstream.

For sanity sake, can I get you to grab one more voltage measurement.
Disconnect the long J3 connector from the X-Pin rectifier board.
Power on and measure the DC voltage at test point TP3 on the rectifier board. Just want to make sure the low voltage at the solenoid driver board isn't because of a bad bridge rectifier on the new rectifier board. With J3 disconnected this test is effectively done with the solenoid driver board disconnected from the rectifier board.

If you don't already have one, you'll need a crimping tool for the connector terminals that are crimped to the wires.

It went up! That's weird. Well the issue isn't the bridge rectifier on the rectifier board then.

Hopefully once you've redone the connectors and changed the capacitors you'll be up and running again.

Dont sweat it, most people make this mistake when starting out. Good to hear its up and running again

Good to hear!
Ok I suggest you dial up the display high voltage to around 180 volts. At 165.7VDC it's putting more stress on the high voltage circuitry because it needs to dissipate more power/heat. There is a little trimpot control above TP2 on the solenoid driver board to adjust the voltage. There's high voltage in the area so be careful not to slip.