Disconnect the wire that comes from your ignition switch at the solenoid.
Then connect the battery cable for a moment. If it cranks, your solenoid has failed in the closed position.
While you have that wire disconnected, disconnect the wire that goes to the starter. It will be about a number 14 wire, comes off the 'cold side" of fender solenoid. Not the one that comes from the + side battery cable.
Hook up one of those electrical testers with a light, or use a test meter on the wire that comes from the key. Measure voltage with key on and then with key off..
If you have zero volts, key off, and 12 volts key on, [or test light stays off/key off, comes on/ key on] then switch is good.
You will need to reconnect the batteries to do this test, so you can have 12 volts go to the key. With the starter solenoid wire off, engine should not crank.
If engine does crank.. your starter has failed at the solenoid mounted on top of the starter.
The wire will be the small wire with the L shaped push on connector.. or could be small lug connector with a nut. The wire that goes to the solenoid on top of starter runs with the big red positive cable that goes to the same solenoid.. if that will help.
I think that should about cover testing what you have happening, and identifying what has failed..
Anybody else see something I've missed?