The first thing to check is to see if the battery is dead. If it is charged, check the battery cables to see if they are tightly connected to the battery posts.
If the battery checks out good, then check the spark plug and the spark plug wire. Sometimes the wire can come disconnected or can be damaged. Check to see if the spark plug is loose or is dirty with oil and combustion deposit. Spark plugs can be cleaned with a wire brush, but should be changed every season.
The model and serial numbers on your Ariens zero-turn mower can be found on the rear left of the frame by the engine.
The model number for your Ariens zero-turn mower will be 6 digits long and start with a "9".
NOTE: if you need a part for the small engine in your Ariens zero-turn mower, there will be a separate model/serial number for the engine. Here are the small engines that are available in your Ariens mower. Visit the page of the engine you have to find out where the model/serial number is located for your small engine model: