Ok, you have a logic problem.

1) If you go to the display test and wait 30 seconds, do you eventually see the 888888 and 999999 numbers show (while all other numbers seem blank)?

2) MPU connector J1 pin 10 has the display blanking signal which goes to all the displays on their pin 10 connector. Can you check if the wire is making good contact at both ends?

Why does U7 - 6810 have 1839 date code on it?
6821 -- U10 is black topped and U11 (also black topped) appears to have 1916 date code on it.
These parts claim to have been made nearly 20 years after Motorola Semiconductor ceased to exist.
I assume U7 is suffering the same problem.
I would seriously start to question your parts source - especially if they are advertising the parts as 'new' or 'original'.

Yes I do.
www.greatplainselectronics.com/products.asp?cat=39
But the 6810s tend to be harder to find as true, unused parts so I don't have those. But I have found a few sellers that have real ones... pricey but real.

The parts on your board are counterfeits. Purposely black topped and remarked parts to misrepresent the true manufacturer and/or age. A vast majority are used parts that have been scavenged from old boards cleaned up and made to look new. The part inside might be the real thing, might not. But with the way the parts are treated during the scavenging process, I wouldn't trust them.
The person you bought the parts from might not know the parts they sold were fakes. But if they're going to be a reseller, now would be a good time to for them to evaluate their sources.

This is high for 5V logic power.
How much voltage do you measure at TP5 on the MPU board and also TP1 on the solenoid driver board?

Ed, this whole machine is a counterfeit of a Bally game. The counterfeit parts just add to the character

You didn't show enough of the displays in your video, but from the little I do see they seem to have the glow under the digits. This indicates the U12 display interrupt generator and also the 6821 at U11 on the MPU board are driving the display digit enable signals ok.

Check the voltages on the MPU board marked with the red arrows below (click the image to zoom in). Also measure the voltages on all the outputs of the U20 chip.

Display_Data_Voltages.png

Sounded like a cheap squeak board on boot up

Something to note - If you happen to have used a 4049B at U14 it needs to be a 4049UB & not a 4049B - a 4049B can cause some of the insert lamps to flicker. The Twobits - 35 assembled boards quite often ship with a 4049B.

It's a rethemed Cybernaut which uses the Cheap Squeak board.

Alessio88 built the MPU board from a blank PCB I believe. Can't tell if U14 is a "B" or "UB" version chip but I don't notice any lamp flickering in the videos.

Yes, there is one wire signal from the MPU board at J1 pin 5 that goes to all displays at pin 8 which controls that digit. So you possible have a bad connection at the MPU board connector J1 pin 5.
Try to swap the J1 pin 5 wire with the J1 pin 4 wire to see if the problem follows the wire.

MPU_J1_Disp_Digit_Conn.png

possible shorted transistor on the solenoid driver board?

This ^^^

BTW I will be working on updating Space Hawks code with freeplay this week. Let me know if you're interested.