Are you sure that when the engine is off that when you stand on the brakes that the pedal doesn't creep down any? But with the engine on it goes to the floor. Weird. I'd think with trapped air it would go down irregardless if the engine is on or not, just easier with it on. Are you certain you are not using fluid? Compare results with engine on versus engine off. Have you looked at the wheel cylinders for leakage yet. I'd bet if you have a leaky cylinder, you will see your fluid go down with the engine on and I guess not with it off. What I really expect is when you push on the brakes with the engine off, the fluid level in the reservoir doesn't move much as you have attested, but with the engine on you can push further on the pedal, compressing air trapped in the lines. Evidence of this, if you can catch it happening, is the fluid level will drop a bunch with the pedal down (or even pump it a bunch) and then pedal off, the fluid will come back up. With a leak, the level won't return to its original level. Did you possibly allow air into the system with the reservoir getting too low? Are your brakes actually working at the wheels with engine off and engine on?