Disconnect J3 and J4 from the rectifier board in the cabinet - this isolates the backbox off the rectifier board.
Power up.
If the 3/4A fuse at F2 still blows, then one of the diodes at CR1, CR2, CR3 and/or CR4 on the rectifier board is shorted, infact you might want to test those diodes before powering up to potentially save another fuse from blowing.
If that fuse no longer blows then the issue is on the solenoid driver board and needs further investigation.

I recommend using your multimeter on the amperage setting (adjust your leads) and test across the fuse clips. No reason to keep blowing fuses.

Just don't hold the leads on forever if it is super high as you don't want to blow your internal fuse in the meter. Usually 10amp but check.

Some folks also have a circuit breaker mounted on a fuse which can be used again and again. I don't find them necessary but they are a cool device.

Thanks
Blake

You'll need to test the three transistors (Q21, Q22 and Q23) and the diodes (CR21 and VR1) on the high voltage section on the solenoid driver board for short circuits although I don't see any burnt resistors in the area which is usually accompanied by shorted transistors.

Note the only time I've seen your particular problem, it was caused by a fault with the big capacitor (C26 located at the top left of your board) causing the 3/4 amp fuse on the rectifier board to blow on powerup.

BTW just to clarify, when you say 3/4 amp fuse, you are talking about the one on the lower cabinet rectifier board right?

Disconnect that large C26 capacitor. Without it, the displays will strobe. If the fuse stops blowing you know it's the cause.

If you do try another solenoid driver board, first disconnect all the displays so there is no external load affecting the solenoid driver board.

Those small brown ceramic capacitors are on a different circuit - they're not related to your problem.

If you haven’t already tried this disconnect all of the displays and see if the fuse still blows. If it doesn’t blow the fuse you have a bad display.

Can you also remove the plastic cover from the solenoid driver board and post some clear pictures of the high voltage components under it?
Also, pull out the 3/16 amp fuse under the plastic and inspect that someone hasn't done an "overfuse" repair on it.

Your working board is giving you changing readings on that big blue capacitor because that cap has voltage stored in it which you're discharging with your meter.
Your non-working board is giving you no reading on that capacitor because it hasn't got any charge in it.

You can't test capacitors in this way, you really need a special capacitor ESR meter to test them. Anyway since disconnecting that capacitor on the faulty board still caused the fuse to blow it tells us the capacitor is not at fault.

Since you have a working board, I would temporarily disconnect the blue capacitor from both boards, replace that broken 3/16A fuse (or for the purpose of the following bench testing only just short it), then on the bench do resistance measurements with your meter on various points in that high voltage section with respect to a ground point on the boards, looking for any vastly different readings between the boards.
Let us know if you find any anomalies.

There are four 1N4004 diodes on the rectifier board (marked CR1, CR2, CR3, and CR4) in the lower cabinet.
With the machine off, test those four diodes for a short circuit with your multi-meter. If one is shorted it will blow that 3/4A fuse on the rectifier board.

However you mentioned in post #5 above when you disconnected J3 and J4 from the rectifier board that the fuse no longer blew which indicates the problem is after the rectifier board.
Has somebody changed the J3 wire connector at the solenoid driver board and wired it wrong?
The display high voltage leaves the rectifier board at connector J4 pin 6 and enters the solenoid driver board at connector J3 pin 6. It's a grey-blue wire.

There's also two ground wires for the high voltage circuit on the solenoid driver board. They are:
Rectifier board J3 pin 6 to the solenoid driver board at J3 pin 22 (black-blue wire)
Rectifier board J3 pin 7 to the solenoid driver board at J3 pin 3 (white wire)

Cool.
Don't forget to clean and put some new thermal paste on the two metal bridge rectifiers under the rectifier board and make sure they're screwed down.