If relay does not "click" then in all likelihood the microprocessor is not even running. Even faulty processor chip will draw some power. That you're reading 0.0 Amps going into the board is not a good sign. A long-shot is to confirm the 5V voltage regulator chip is generating 5V DC. The processor circuit needs 5V to operate and if there's no 5V there's an every-so-slim chance the replace-able and inexpensive ($1) regulator chip failed.
So if you're still up for some DIY troubleshooting, you can probe the chip to confirm unregulated DC going in, and 5V regulated DC coming out.
I'm not familiar with your specific engine but somewhere there's this regulator chip screwed to a heatsink with red, blk, ylw wires as shown. You can pull back the white housing to expose the regulator pin (as shown in photo) while still making contact to the long pins of the chip. Measure the DC voltage going into the chip relative to the GND or metal tab of the chip. This GND is NOT the same as the chassis. The IN DC voltage should go up and down as you change track voltage and will be tad more than the AC track voltage in magnitude. But the 5V out (again measured relative to GND) must be 5V DC. The hope being this chip failed and there's no 5V OUT. A long-shot to be sure but this should only take a few minutes to try.
Otherwise I'd say you need to consider your options - upgrade to new board set, send to GGG or whomever for evaluation/repair, whatever.