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Find the solenoid on your lawn mower. Trace the large red or positive cable that comes off the battery to the first junction to which it is connected. The battery cable will end at the solenoid and be connected to an electrical post. Leading away and on the other side of the solenoid will be another large red cable. This leads to the starter motor. Although there will be one or two other wires connected to the solenoid, none will be as large as the battery and starter cables.
Remove the starter cable from the solenoid by using the proper sized wrench. Keep the battery cable mounted and in place.
Set your multimeter to 20 volts DC. Turn the ignition to "on" and touch the black or ground probe to the chassis, and then touch the red or positive probe to the post where the battery cable is connected. Read the multimeter and verify that there is a voltage reading of approximately 12 volts.
Remove the red probe from the battery side, and touch the electrical post where the starter cable has been removed. Turn the ignition to the "start" position and read the voltage on the multimeter. The voltage should be exactly the same as on the battery side. If there is no voltage showing, the solenoid is no longer working and needs to be replaced.