Bad brake booster?? Please help!

I had great luck with my last posting, and I hope this will yield the same!

Background for problem:

When I was changing my wheel bearings, I didn't clamp the brake hoses because they seemed brittle; instead, I just put a block of wood in between the pistons when I removed the caliper. I went to bleed the brakes. I didn't realize the block had fallen out, and consequently the pistons fell out. I got them back in okay, and the seals seemed fine. Later the same night I managed to break off a bleeder screw another caliper, and ended up replacing the caliper another used one.
I went to bleed the brakes again, pushing the pedal all the way to the floor, which I later found out, you aren't supposed to do. I thought I had ruined the master cylinder, so I replaced it.
My brakes still don't work. I've bled the lines at least three times and there is no air, and there are no leaks. The pedal is quite stiff after bleeding, but as soon as I start the car, the pedal is very soft, and stays soft in subsequent sessions - car running or not. Also, when I tried hitting the brakes while driving (To see if I would make it to a mechanic which I realized it wouldn't) there is an audible and tactile (pedal) rumbling sensation that was never there before, which seems to be originate from the front driver caliper (the one with the pistons that fell out).
The only thing I think is left is the brake booster, but since I'm not sure how they work, I don't know if this is accurate.
Any suggestions or shared knowledge would be most appreciated.

Jeff