When you turn the Ignition on to start are you actually getting voltage where the wire from the Ignition switch connects to the Starter solenoid? And, when you do that with the volt meter you can verify what voltage you are getting.

I know you feel you covered that at the connector but that is not exactly the same.

It might be that you actually have to remove the wire from the from the ignition switch to the solenoid to be sure it is making good contact with the solenoid terminal. Since the alligator clips may be making a different contact.

If you are only hearing the click from inside of the Car it is possible you are hearing something else click. Have someone turn the key while you listen with the hood open so you can hear exactly where the sound comes from.

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84 300D, 82 Volvo 244Gl Diesel