You can't accurately test a mosfet in-circuit.

We're really talking more about the diode than the coil. If the diode was shorted then the coil would still work but you would get high voltage feedback to the board, which could cause a reset or other problems. The most common reason for a diode getting blown on a coil is being installed backwards or the driver transistor locks on.

You really need to monitor the 5V while you're playing the game. If that's the problem it's likely only dropping under load. You will need a decent meter to catch any fluctuations since they'll be pretty fast.

Should be a test point on the mpu.

Are you putting one lead on pin 2 and the other on pin 3?

To check the 24vac you want one lead on pin 1 and the other on pin 2. Then one lead on pin 1 and the other lead on pin 3.

Make sure all of the coils have diodes installed and the diodes test good.

In a DC circuit you have a positive and ground so readings can always be referenced to ground. In an AC circuit you have hot, neutral and ground. To get a proper reading you want to check from hot to neutral. Just the way AC works vs DC, current flows in one direction in an DC circuit and is bi-directional in an AC circuit.

Not sure how you're taking this reading. If pin 1 to pin 2 is 24v and pin 1 to pin 3 is 24v they you're good. If you want to see the 48v then put one lead on pin 2 and one lead on pin 3.

It's extremely unlikely it's the transformer. Just like coils they work or they don't.