Brake Pedal Goes to Floor When Car is Running

The booster is just a vacuum powered way to increase the available power to push the pedal, so saying it goes to the floor when running but fine when the car is not running makes a person that knows how it all works go, Huh?
(We understand what you mean, but it's not actually possible for both to be true)

Power brake brakes are stiff as hell when they don't have power to them.

Start with bleeding from the farthest wheel from the master cylinder and work your way to the closest wheel to the master.
If that doesn't do it, step on the pedal with the car running and set your emergency brake.
Test the pedal again.
If it feels alot better with the e brake set, then the rear brakes need adjusting.
(Setting the e brake takes all the free travel out of the rear brakes, basically eliminating them from having to travel when the brake pedal is applied)

The fact that the pedal goes to the floor only when running tells you that the booster is working.

What I suspect is air in the fluid (like already mentioned) or too much travel needed by the rear brakes from way to much play in the rear adjustment.

Just a note:
Most people don't know that these brakes have an automatic adjuster in the rears that when you back up and apply the brakes it moves a plate that is supposed to turn the adjuster.
Sometimes they work, and sometimes things are to dirty or worn out to work.
I any case, when the rear brakes are a long ways out of adjustment it would take 30 or more backing up stops to get them back in adjustment.
(Don't try this with yours if the brakes go to the floor) It was just meant as an FYI.