Before you start check you have the correct starter they come in clockwise & counter clockwise rotations and several different sized sprockets.
One incorrect combination will jamb when engaged and thus toast the starter.
Now for testing
Start by running a heavy jumper from the - battery terminal to the oil drain bolt.
If things start to work, clean/ replace te earth strap
Do the same with a + lead, first to the solenoid hot wire, second to the switched wire on the solenoid finally to the starter.
Same story any place when a drastic difference is noted, clean or replace the wire.
Next to the solenoid proper
remove it, clean up the base and the mounting bolts and the mounting bolt holes.
If it is OEM then it earths through the body by a mounting bolt check this by running a jumper from the battery - to the body of the solenoid.
All this checks out then run a + wire to the starter solenoid trigger terminal, verifies the solenoid
Run a wire directly from the S terminal on the switch to the trigger terminal on the solenoid, verifies the switch.
from there it is a matter of trying the jumper to both sides of the pto switch , parking brake & neutral switch.
All the start safety switches are normally open & close to complete the loop from the start switch to the solenoid trigger.
These wires are generally pink, yellow , orange or red with a tracer and may change colour at the switch plug
