First, you might want to make certain your cables going to the starter are in good shape (no worn insulation spots- generally caused by rubbing or flexing) and the terminal connections are clean & not corroded plus check your battery terminal & connections then clean battery negative ground cable at both ends (battery & ground end).
I memory serves me right these units have a starter solenoid, when these go bad you can have a no starting issue - you can jump the solenoid terminals & activate the starter - be careful when doing this - used to do this often on my first $150 car a '51 Ford when I didn't have the coins to buy even a good used one.
And as I recall the manual transmission units (you call a shuttle tranny) did not have a neutral start switch only the units equipped with a torque converter transmission (aka Power Shift transmission). I used to work at Allis Chalmers lift truck plant and my first job in '67 was writing parts, service & operators publications for these trucks.

A quick check on your battery is to test it with a volt meter after it has been charged. Battery voltage should be at least 12.6 volts after the battery is taken off the charger & has sat for several hours to cool down & avoid getting a surface charge reading (which is always a bit higher than actual).