What happens when a solenoid on a lawn tractor goes?

Answer 1

Most likely, it won't start.

The solenoid is merely a high current switch triggered by a low current electromagnetic coil. It consists of the the large, high current connectors and a piece to connect the two so that current flows (to the starter) usually done with a roughly "T" shaped piece using the top part of the "T" as that connector. The vertical part of the "T" is surrounded by an electromagnetic coil to move it. The low current post attach to the coil and, when they have voltage present, throw the top part of the "T" into the high current contacts. When no voltage is present the contact is broken by a spring that moves the contacts apart. Often one half of the low current part of the circuit is built into the frame of the solenoid so that the ground part of the circuit is achieved by bolting it to the machine frame. Other times it is separate and used in some fashion in a part of a safety circuit.