Allow me to clarify:
The caliper was off the rotor because I was changing the wheel bearings. During the bearing replacement, I hit the brake out of habit when I was getting in the car. The block of wood I had placed between the pads had fallen out and the pistons fell out of the caliper.
I've been bleeding the brakes with a second person while making sure both compartments of the reservoir is full.
I don't plan on driving the car until I get this fixed, but I am really hoping to solve this myself. I've already eliminated the possibility of a bad master cylinder, initial hydraulic pressure (before the car starts), and possible one caliper....