As LTG stated the door buttons not working isn't because of batteries per se. Check the coin door interface board and all the wires going to the coin door switches and make sure there's not a broken wire somewhere, you could also use a jumper wire to simulate the escape switch at the MPU. Since these are dedicated grounded switches they are not part of the switch matrix and you don't need to use a diode to simulate closing one.

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Yeah, no 12VDC will kill all switches so you need to figure that one out first. Do you have 18V (LED 6)? Have you checked F114?

I'd be surprised if it's the fuse holder, more likely a bad BR1 bridge but you can test easily enough in AC Voltage Test. One lead on J101 pin 7 the other on both sides of F114, you should have ~13VAC with the lead on both sides of the fuse. If either filter cap were bad or the bridge shorted it should blow the fuse but if the bridge is open you'll have less than 18VDC. Lots of references on how to test the bridge in circuit with a meter in diode test.

Put fresh batteries in and measure DC voltage at the banded side of D2, if you don't have ~4VDC or higher measure the anode (non banded) side, if you have voltage there you have a bad diode, if not you have a bad battery or a bad contact in the holder.