What does the battery read across the posts when you turn the key to crank?
Do you hear a distinct 'click' when you turn the key, slowly, toward crank? If you're battery voltage drops from say 12.5 or therebout when you reach crank position, to 11 volts or less, your battery is not supplying enough amperage to get her to crank over.
Also, depending on hours on the machine, (which are currently?), the ground cable to the chassis may have adequate corrosion to keep it from starting. Check both cables at the battery posts, the chassis, etc., and make sure there is no corrosion inside the cable sheathing near the ends.
The key switch itself could also be bad/flakey, they have at times been problematic.
Report back results on everything else first. Once you have stop solenoid loud click/clack when turning the key toward crank she should start, OR you may have key switch/relay issues. one step at a time.:thumbsup: