Well, if the voltage you measured is dropping to zero, that means that something is wrong between the starter solenoid and the battery (i.e. wiring, connections, switches, relays, etc.). What that is telling you is you have excessive resistance someplace in the circuit feeding the starter and that resistance times the current trying to flow to the starter is causing a voltage drop. So a new starter is unlikely to help.

Would kind of like trying to run a big V8 engine with an eyedropper feeding fuel to it. Sure, the engine would not run, but not because of a problem with the engine, rather that it is not getting enough fuel.