That second cable at the starter is expected.
When you use that screwdriver.. it should make the starter work. If you removed the ground cable.. it's not going to work w/o that hooked up. Put all the stuff you unhooked etc, right back where it belongs and give it a try. From there we can quickly diagnose why it's not starting through a few quick tests.
The screwdriver is to see if the starter is good because it removes the pcm, relay etc etc from the equation. Once we know the starter can turn the engine, then we work our way backwards from there by testing the purple wire for power of 12V. You mentioned a very low voltage of 1.8-2.4, this tells us you either aren't getting power to that wire or you aren't getting a good ground. If you had stuff unhooked while you were testing that... then it's not a good test that we can rely on.
I think in your year the ignition switch sends a signal to pcm to crank engine. If the pcm sees the car in park or neutral it should send a ground signal to a relay that then engages and sends power to the purple wire of the starter. This may be as simple as a crusty relay or bad contacts in that relay. However you don't see many bad relays, it's usually something causing the relay to not be actuated.
