Hi. Yes you should have 27VDC at the brown-orange wire. This is coming from the red wire through the relay coil,and the 27VDC should be present all the way to the driving transistor.

Since you don't see the 27VDC on this side of the relay, you have a problem right at the relay board. Could be an open coil, broken through hole lead under the relay for the relay coil, broken through hole pin on two pin connector for the relay coil, burned or open trace, or failed wire crimp connector. Removing the board and examining with an ohmmeter should quickly identify the fault.

Maybe this visual will help you understand better. In a correctly working pin on the left, the collector of the transistor "switch" will have the source voltage of the solenoid present. This source voltage is present along the entire circuit. When the transistor switch is operated, current begins to flow . In the defective circuit on the right, there is no voltage at the collector of the transistor. Therefore, if even if the transistor driver circuit is operational, there is nothing for the transistor to switch, so no current flows. The driving transistor at the CPU or driver board does not supply power, it PROVIDES ground when turned on.

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Your welcome. Not strange at all. The vibration stress on a machine can break all kinds of things. Mechanical relays generate internal mechanical stress. You might find cracked solder around the through hole pins underneath. You might unsolder the relay and see that a lead has broken off. If the relay was stuck on the coil could be damaged. And....you don't know for certain if there is a secondary problem or not until this first problem is resolved.

When no current is flowing (circuit path is incomplete) both sides of a resistance will be the same voltage.

The relay coil resistance is high, but did you pull the relay board to check all those through hole connections? You would have near infinite (open) to come up with no supply voltage on that side of the relay when the motor control is not active.

Yes, that relay and looks like the same shape part. It's a standard 24VDC relay, as long as footprint iand pinout is the same, . nothing else is special about it.

When there is no competed circuit path, no current flow, resistance does not cause a voltage drop. It doesn't matter if the relay coil measures 10 ohms, 1000 ohms, or even 100,000 ohms. You should still see source voltage on both sides of the relay coil. Only an open circuit on the relay board will produce the symptoms you have described. This is basic electronics theory.

Some people here have accomplished great repairs without electronics knowledge, and others have made the process more difficult or even damaged games.

I'm just one of the few here with formal electronics training and years of career electronics experience.

That looks ok. You could assume the relay is bad, or you could go an extra step and use a test lead to jump the plus +27 (red wire) to the power pin #1. The coil trigger pin #2 should measure +27VDC. You could then ground pin #2 and listen for the click of the relay. Another step further, measure the output pins 1 to 6. They should be open (near infinite) resistance, and then change to low ohms when the relay is activated.