Your 4710 is one of the "Ten Series" tractors and shares the same technical manual as the 4510, and the 4610 that I have.
One of the improvements of the Ten Series tractors is a re-design of the fuel shutoff solenoid circuit to get rid of the "thermistor" (really a resettable thermal fuse) used in the earlier models, so that shouldn't be your problem.
The 4510/4610/4710 do have a new module called a Fuel Solenoid Timer Module which plugs into the fuse/relay box and replaces the "thermistor". It seems to be an improvement in the circuit design, but that module can also fail, and I had to replace mine at 1150 hrs.
Let's not speculate on failure modes just yet. The first question is whether or not you hear the loud clunk which occurs when a properly operating fuel shutoff solenoid retracts when you turn the key from OFF to ON(Run). If you don't hear the fuel shutoff solenoid retract, then the engine will never get fuel and will not start.
If you want to test the fuel shutoff solenoid, simply unplug the 3 contact plug (near the fuel injection pump) and measure the resistance of both the hold-in coil and the pull-in coil. BTW, it is common for the A to C measurement to be closer to 24 ohms than 12 ohms, and is not a problem if it reads that high.
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Agree with others that it is important to have a good battery and also to let us know if the tractor is flashing any error codes. You seem to actually have 2 problems, but the first step is probably to get it starting again.
There are two error codes associated with forward/reverse pedal voltage being out of range. If either error condition exists, it would prevent movement in either direction.
There is another error code that flashes if you press either pedal when the seat safety switch is not closed. This would also prevent movement in either direction, so check your seat safety switch.