Get a simple voltmeter. Analog is best for this, as during a dynamic situation like starting, you can get a feel for how much the voltage drops to when the attempt to engage the starter occurs. Get another person to sit in the seat and operate the key. You put voltmter Directly on battery posts, NOT the battery clamps... Directly on the posts. What does it read? 12.6 volts? Hopefully within a range of 12.0 to 12.6..If it is reads below 12 volts, the battery could stand charging.
Have assistant turn on the headlamps. You stay on leads on the battery posts NOT the battery clamps. What does it read now... If it drops significantly while you are on the battery posts.. this indicates a discharged battery. Have assistant attempt to start tractor while you stay on the battery posts with the leads. What happens now? Chattering sounds.. What does the battery voltage drop to on the posts? Sigfificant drop? 10.5 volts or below? Discharged battery. Does the voltage stay up near 12 volts during all of these tests? Probably not the battery.
NOW move the leads over to the battery clamps. Does the voltage stay near 12 volts when the above tests with headlamps and starter attempt is made? If not then you have a high resistance between posts an clamp. Take em off an clean em up. Still have problem? Still wont't start. Possible high resistance in battery cable or cables.. That is a common problem. Also negative cable to frame of tractor high resistance is a common problem.. You can take voltmeter between a good clean frame point and the negative terminal of the battery.. It should measure 0 volts in all cases... Do you read voltage between negative post and frame? You have a connection problem forming a high resistance.
All of this takes far far longer to type out and read than it does to make these tests.. You should have an answer in a few seconds with a simple voltmeter and some knowledge.
If you were to ask me what are the chances.
1: Battery discharged, or defective, usually from buildup of sponge lead in bottom of the cells. This is the most likely things.
2: High resistance corroded battery clamp. Corroded cable internally, or bad connection to frame in that order. maybe one chance in 3
3: Defective starter relay, and or starter solenoid.. This is not very likely, about 1 in 10 or less but it is possible.
4: Starter? Not a chance in "heck"... Don't go hitting it with no dang hammer. You don't have a draggy starter.. one chance in 1000. Jeez.. a 3 pound hammer no less...