How to check
Have you a multimeter? There are two terminals of interest in the starter, a large one with a cable, perhaps #4 or #6, going to the starting battery, perhaps through a switch or selector. Assuming any applicable switches or selectors are in the correct position, this cable should be energized. Connect one lead of the meter to ground, like a clean spot on the engine or alternator. Touch the other lead to this large starter terminal. Should see the battery voltage, nominally 12V. The smaller terminal is a spade lug on the starter solenoid, the mating part on the wire. This wire is energized when the starter button is depressed or the key is turned to "start," depending on how the system is wired. Touch the meter lead to the metallic part of this terminal while an assistant attempts to start with the switch. This terminal should go to 12V. If it does and you don't hear the solenoid close and the starter at least try to turn, it's the starter. If not, the wire is not being energized due to a fault: switch, wire, or fuse. You can verify that the starter works, or even start the engine by jumping with a test lead the large terminal to the small, momentarily, just as you would with the starter switch. If it is the starter, and you're not knowledgable of these, you have a few choices: a new one from Universal for $1035.00; from a Kubota dealer for just under $300.00; a Valero, Denso, or other equivalent replacement for from $99 to $200; or a rebuild/repair on your old one at a shop for probably around $50 or so. There's a shop in Hudson, MA called Automotive Components that can do it. There are many others. If you do any of this, be careful! You could be hurt. The engine could start, and if you have your head or clothing or any tools or wires in the way they could be hit or become tangled in the fan belt or alternator fan and pulley. Don't ask me how I know! Also, the battery lead may not be fused, and if you inadvertently short it to ground you can draw enough current to burn yourself, or weld the shorting instrument to the terminals. A persistent short could cause the battery to explode (though not likely).