The solenoid on a riding lawnmower is used to start the mower through an electromagnetic switch. When this switch isn't working properly, the mower will not be able to start. This switch will close when the ignition key is turned, which allows electricity to get to the starter and start the mower. If you are having problems with your solenoid, you can test it yourself with little hassle.
Turn off your riding lawnmower and take the key out of the ignition.
Open the bonnet to your lawnmower and locate the battery. Look to the side of the battery for a small black box; this is the solenoid. You should see a red wire connecting the battery to the solenoid.
Look for the two large posts on the solenoid. The red wire will be connected to one of these posts. The other post will have a wire leading to the starter.
Bridge the gap between the two posts with an insulated screwdriver. Look at the starter to see if it spins. If the starter starts to spin, your solenoid has gone bad.