Tom,
It **sounds** like a neutral safety switch issue to me. There is likely one on the PTO lever, the seat, the clutch and sometimes on the emergency brake. Need to check each one to make sure they are operating correctly and haven't become detached or damaged. At the very least, try wiggling each of the levers while holding the key in the start position to see if she cranks.
Assuming the neutral safety switches are fine and you know with 100% certainty that they are not the problem, then I'd proceed as follows:
First thing I'd look for is a blown fuse either in a fuse panel or inline with the wire that runs down to the starter.
Next, jump a small wire from where the positive battery cable attaches to the starter solenoid to where the other small lead attaches to the starter solenoid. If the solenoid and starter are good, the engine will crank. If it doesn't then you have a bad solenoid or starter.
Assuming the engine cranks, then follow the small wire back to the key switch or start relay. Often if the tractor has been stored outside, the key switches end up going bad. Look carefully at the terminals on the back side of it to see if they are corroded or have loose wires.
The next test you can do is to jump from the positive battery terminal to where that wire that runs to the solenoid connects to the key switch or relay. (make sure you reconnected the wire to the solenoid that you disconnected in the above step). If the engine cranks when you jump to that terminal, you know the wire is good to the solenoid. If not, then you need to follow it to figure out if there is a fuse or break in the wire.
Finally, some of the models have a starter relay. Those also go bad. To determine if the relay is bad, you need to figure out if it's getting power from the key switch when the key is turned. You'd use a multimeter for this with the black lead attached to ground someplace, and the red lead attached to the power feed wire that runs from the switch to the relay. If you turn the key and it feeds juice to the relay and the starter doesn't crank, then the relay is suspect.
Again, check the neutral safety switches very carefully. They are usually wired in series and when they're all closed they provide the ground for the start relay. If one is open, the relay won't engage because it doesn't have a ground. This might lead one to think the relay is bad when it really isn't.
I don't have a schematic for your model tractor, so I don't know for sure if yours is wired this way or not. The instructions above are me winging it, but they will help you determine where the problem is.
Finally, you can order a manual online from here:
http://www.messicks.com/Wiki/Kubota/B1750.aspx
Hope this helps,
Steve