Hey! Got directed here from your email. Nice the thread gives a pretty accurate idea of what's going on.
Here's how this works. RC5 is a resistor capacitor network that holds the value of Coin 1 and Coin 2 high until it gets shorted by the coin switch. That is, it keeps the line at 5V, until the switch closes and it becomes 0V. If anything is wrong with RC5, the input line "floats." This means the cabinet wiring basically becomes an antenna and any stray noise can trigger a coin input. Alternatively, if RC5 is not working, it cannot coin up because it cannot toggle between 5V and 0V, because nothing is giving it 5V. RC5 is the most likely cause.
The "input chip" is 8A, the 74LS367. This chip interprets these 5V / 0V transistions and puts the information right on the data bus back to the processor. Since this is the main data bus, and you aren't having any problems booting, this is why we think there is not a problem on the data bus and it is possible you are having a problem with 8A.
It is unlikely, although possible that RA3 is bad, but I doubt it, even though I said it was likely in the email. I think it is unlikely because it sounds like your other inputs are working properly, and the thing boots.
A third option would be chip 73LS138 at 3A. This chip determines which input chip (4A, 5A, or 8A) gets read. If the enable line is not strong, you will have intermittent problems with both coins, and player 1 and 2 select buttons.
I am referencing this schematic, page 5
https://www.arcade-museum.com/manuals-videogames/G/Ghosts N Goblins Schematics.pdf
All that to say, replace one at a time:
RC5,
8A
3A
in that order and I would be shocked if that didn't resolve the issue.
-GB