To Clarify this, the Displays are probably out. Either outgassed, or high voltage section failure; so you are unable to see that they probably say adjustment failure, indicating that the batteries on the CPU went dead, and the machine is awaiting you to enter diagnostics to set pricing and other features.

try tapping the test/reset button on the cpu board and see it the machine doesn't at least go into attract mode (lights dancing), and then the coin switches should add credits, and the you could try to start a game.

Optionally, you can hold down the adjust select button after tapping it a couple of time, until it cycles through all the adjustments, or the dirty method of quickly flicking power off the on again to get it to boot.

If it does, then you're at fixing the battery issue, and the display issue, which are both probably expected failures for the condition of the machine when you got it.

You would at least know where you are at if you can get it to continue on past the adjust failure it probably has on the screen you can't see, if the cpu really goes to a status 0 when booting.

That hacked rouge board looks to be some kind of timer board, there is what looks to be a 555 timer at one end, and the other board goes to a couple of relays. They were probably using this to try to get around the same battery issue at some point in the past by quickly resetting the cpu; and the switch probably reset the timer as well....

What wires is that thing spliced into?