The sequence should be:
1. apply power to the solenoid
2. solenoid engages, shoving the gears into place and making the big connection to the starter motor itself
3. starter motor turns engine
you can try this:
attach an analog voltmeter to the high amperage connection between the solenoid and the starter motor. when you 'crank' the engiune, what voltage is present? In a 12V system, should be 8-10V, twice that if it is a 24V system.
maybe try this to test the items of the starter separately:
1. disconnect the high-amp link between the starter solenoid and the starter motor.
2. energize the solenoid either by the starting switch or by applying power to the solenoid.
3. Does the solenoid 'clunk' and engage or try to engage?
4. next, test the starter motor.
5. attach a high amperage cable to the starter motor hot terminal. Maybe you can use a cheap jumper cable.
6. connect this very briefly to power. (do not do this for more than 1/2 second or so, or you can overspeed the motor)
7. Does the motor spin?