Have you checked the battery voltage while someone else tries to start the car? Look for low battery voltage, and also check for voltage drop in the battery cable to the starter and check the ground cable for voltage drop. Put you digital voltmeter probes on both ends of the cable you are checking for voltage drop.

If you are getting the necessary voltage (and therefore, current), either your solenoid is not making good contact (across its points) or you have a problem with the brushes, commutator, etc. Be sure to check the braided wire connecting the solenoid to the starter for a tight connection at the solenoid.

I have had both good and bad luck with rebuilt electrical products.