When turning the ignition to START, a "clunk"/no start indicates either a
weak battery, bad starter contacts, bad battery cable, or bad starter motor.
If you hear nothing when turning the key to START, that's either a REALLY
weak battery, a bad ignition switch, a bad starter relay, a wiring problem
somewhere, or a bad starter solenoid.

In your case, given what you've eliminated, it certainly sounds like your
starter solenoid is bad/sticking.  I'm assuming that if you have someone
else turn the key, and you listen to the starter relay, you can hear the
relay clicking.

Disconnect the battery, then remove the starter (pretty simple - just three
bolts).  On the bench, ground the starter, and then apply +12V to the
solenoid terminal (the terminal with the smaller of the two wires that was
connected to it - not the big cable that came from the battery).  You should
get a 'clunk' from the solenoid engaging.  If not, and if you can't do it
consistently, then it's time for a new starter.

Clutch interlock switch if it's a manual.
Steve