Something don't sound right - you say you can rotate the engine via the rear wheel - how easily and in what gear?? Realistically I would expect it to be almost impossible to turn the engine over due to the very high compression.
The knock you hear when the starter button is pressed would I expect be the starter motor teeth engaging the flywheel - but for some reason the starter motor may not be turning over. This would be something in the starter mechanism, maybe wiring within the starter motor, earthing, or corroded contacts or similar. If that is proven to be the problem you would need a r&r of the starter motor.
Or a thoroughly jammed engine, though unlikely if you can turn it over via the rear wheel.
Check that the engine *can* be turned over (best to remove the plugs to do this), otherwise check the starter motor is functioning correctly - to do this properly would it would need to be removed and bench tested