I think your on the right track, the processor is in blanking (not booting) and flashing you the RAM failure code, your +5V could be low or there could be other issues with connectors or ribbon cables causing this that can cause blanking but these wouldn't give you a RAM failure.

You actually have a lot of options here, I would check voltage first as this is just a good practice. If I suspected the RAM, I would simply pull the CPU boards from both ADDAMS and STTNG and simply swap them into the other machine; obviously you will need to swap the ROMS on both boards. On the board that came out of STTNG, I would press down on ASIC and processor before installing it in ADDAMS; at this point if the original STTNG CPU board is still flashing a RAM failure you know its the issue.

Good Luck

EDIT: Was this already done? I just noticed that the CPU board you currently have in STTNG has a Bally-Midway 20017 Serial Number label on it meaning it came out of an Addams Family machine

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First thing to try is always reseating the MPU Ribbon cable on both sides

Do that a couple of times (gently!!) to wear down any corrosion. Also check for battery acid damage. I had a SS which flaked out ON THE DAY I was selling it because of batter damage

In the diagram the highlighted yellow dots are Test Points (TP) where you can measure the voltage with a DMM - the red writing in the diagram next to the TP is what voltage you should expect. There are also red dots highlighting the various LEDs on the board, these give you a general indication (the below shows what each LED is for) however measuring the specific voltage with a DMM at the TPs can help pinpoint an issue

WPC Power Board LEDs (resized).JPG

Yellow are voltage test points, red are the LEDs associated with the test point numbers.

A small bladed screwdriver works very well but I like this tool better:
https://www.amazon.com/Wiha-26810-5-7-Inch-Precision-Lifter/dp/B00433SJB2