There's no need to have the car running, to bleed the brakes, if the car has power brakes. Once the vacuum is released from the booster, you've got direct contact with the MC piston, bleed away....that being said, I'm strictly referring to vacuum assisted power brakes, I have no idea if a hydroboost set up requires a different procedure.
The mention of ABS is spot on, as that can impact how brakes need to be bled if the lines are cracked pre-ABS module. One of my cars has a specific tool for that, it does that among other things, and it's pretty expensive for a typical DIYer to run out and buy. The fact your pedal keeps going to the floor means one of two things - a massive amount of air in the system getting compressed, or as mentioned prior, a leaking MC piston.
Another option, if any local parts stores have them for rent, is to get a pressure bleeder, and bleed again to see what comes out. When used properly, those make the tedious process of bleeding brakes a walk in the park.