I replaced the high / low switch and reverse gear in John Deere 4020 tractor. Once I replaced the high / low switch and the reverse switch fell over 2 weeks later.
You can also get Peg Perego Gator Shifter that improves the vehicle.
Motor off, lift the drive wheels and check if the transmission is locked.
The parking brake switch is the most likely culprit, any other would cause the tractor to not rotate in the crank position.