I have to concur with Chris1956's assessment. And I say that because in your initial comment, you stated that even if you rope pull start the engine, the starter spins. Since you haven't energized the starter via the key when pull starting, it has to be a problem with the starter solenoid. Otherwise the starter bendix would be out touching the flywheel.
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Look at the starter before even inserting the ignition key. Is it touching the flywheel? If no insert the key and turn it to on, not start, but on. Now look at the starter. Is it touching the flywheel now? If so, you have a wiring or ignition key issue.