If that machine uses a hydraulic drive pump, it has a safety on the pump to disengage the hydraulic drive when the breaks are hit and when you are starting it. This typically has a foot pedal brake sensor and a drive position sensor to stop it from cranking while in gear. Will your machine drive with the motor running and the key in the stop position. Does the brake pedal work to stop the machine? Did you try turning the key to start with the motor running does the starter engage or does the power system turn on. Do you have work lights, with the key off?
Does your machine have a electrical fuel shut off solenoid? How does the motor cut itself off when you turn the key off. Mechanical fuel shutoff?
If your machine has a wiring harness it probably has several of these items. My grader has more things going on in it than I realized. I had to figure out how to get the drive going once I figured out how to crank the motor.
How did your motor start by jumping the solenoid without turning the fuel on? Key on, fuel solenoid on??
If I turn on the fuel and bypass the key with the 12v to the starter solenoid on my machine, I must turn on the key to the start position (not the run position), it will not try to start but it will send power to a relay somewhere. Once this occurs, all lighting and the charging circuit works. If I turn off the key switch the motor will keep running since I had to remove the electrical fuel shutoff solenoid, because it decided to melt in the middle of a critical grading job. I must manually kill the motor now, the lighting circuit stays on even when the key is off, until the motor is shut off. The generator/ alternator is powering everything until the thing stops turning. My machine has a warning alarm that sounds if the key is on and the motor is off.
In order to get my grader to drive I must energize the safety on the pump. If I do this I loose my brakes and the motor will keep powering the pump even with the brakes applied and it does not want to stop. I can not let anyone use my high tech machine for fear they will freeze up and not be able to control it in the heat of the moment.
I had to figure all this out, without a manual, while it was sitting on a trailer with 20 guys looking at me wondering why I was not working.