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Most likely the solenoid is your problem. The only test that you need to do to make sure is to test the voltage at the small wire going into the solenoid from the ignition switch. When the key is turned to start you need 12 volts coming from the ignition switch to charge the solenoid and put voltage to the starter
Correct. If you do not have voltage at this wire then something is causing the ignition switch not to work properly. I would start by checking the safety switches. There should be one in the seat, one at the brake pedal and one on the blade engagement lever. All three need to be in working order to make the engine crank