If you've not already, isolate the starter and start from the minimum and work your way up.
1st - Using jump cables (earth on starter case, live on solenoid bolt fitting) and a thick wire (from the solenoid bolt fitting to the spade connector on the solenoid, closest to the engine block when fitted), test the starter function from the battery in the car, with the starter not mounted to the block - secure it on the floor with a foot as it can give quite a kick... The starter will 'fire' when you put live on the solenoid spade connector, assuming it has earth and live too.
If this works then:
Fit the starter, but do not connect any wires from the car - use your jump cables and the thick wire to test the starter, make sure you use one of the jump cables as an earth onto the starter case.
If this works then you have a problem with the vehicle wiring somewhere.
First, remove the earth jump lead and see if it still starts when you put live on the solenoid spade connector
If this works, then re-connect the spade connector on the solenoid that goes to the ignition switch and try to start using the key
If this works then remove your live jump cable from the battery to the solenoid bolt fitting and re-fit the live wire from the battery clamp, but not the one from the alternator.
If this works, then refit the wire from the alternator
Hopefully you'll find that at the start of these troubleshooting steps when you're not using any of the vehicles wiring, the starter will work ok, but at some point along these steps it will stop working. If this happens it will point to the problem.