Say hypothetically, I wanted to rig the starter up to a push button activation.

Okay, there are 3 contributing factors to making the starter work.

1. Is the starter cable. This is the cable that connects from the battery to the starter.
2. The grounding, the grounding is grounded on the engine block.
3. That wire that connects to the solenoid.

Now Right now, I have a power wire hooked up to the starter cable, and the engine grounded out, so there is a 12 volt system running through the car.

I then have that wire that connects to the starter soldnoid. Now when I touch it to a +12v source, it makes a noise but doesnt crank over.
When I touch it to the negative source, it does nothing.

Am I missing something, or should it crank over.

 

When you say you have a power wire hooked up, are you saying you have physically added another wire going from the battery straight to the starter without any interruption?

 

Connect the starter negative to the frame or battery negative, that will be much better than the engine block.

So, like you said, battery power to starter, ground to starter, then a signal to the solenoid will trigger the starter. Some of them have 2 connections for the trigger, so you might check that.