Open the hood of the tractor by leaning it forward over the front end. Look behind the dash kick panel, and locate the inner end of the ignition switch. Check the wires to the switch to make sure they are properly connected, and not burned or melted.
Turn on the multimeter and set the dial to "V" for volts. Attach the red probe from the multimeter to the red wire on the inner ignition switch wiring connector. Attach the black probe to the black wire on the same connector.
Ask your assistant to sit on the tractor and make sure the gear selector is in the "N" position. Tell him or her to turn the key to attempt starting the mower. Make sure your hands and feet are away from the moving parts of the engine. Read the multimeter as your assistant turns the key. If there is a voltage reading and the mower will not start, then the ignition switch is malfunctioning. If there is no voltage reading, then there is no current going to the switch -- proceed to Step 4 if there is no current going to the switch.
Trace the wiring harness with your hands to the chassis, about one foot from the ignition switch. Locate the small box attached to the wiring, on the left (sitting on the tractor) side of the engine. This box is the neutral safety switch. Attach the red probe from the multimeter to the red wire on the safety switch. Attach the black probe to the black wire.
Ask your assistant to make sure the gear selector is in the "N" position, and try to start the tractor. Keep your hands and feet away from moving parts of the engine. Read the multimeter as your assistant turns the key. If there is voltage to the neutral safety switch, but no voltage to the ignition switch, then the neutral safety switch is malfunctioning. If there is no voltage to the neutral switch, then proceed to check all of the ignition wires, the fuse panel, and the ignition circuit breaker.