when the car is off and I bleed the brakes, and then I check them-- they are fine. But when I start the car and check them, the brakes go to the floor. Could someone please help me?

It sounds like your Master Cylinder is bad. It appears OK with the car off because you don't have the added pressure of the power assist, but when it's running, it shows the leak. If this doesn't work, check out the power assist. I'd try the MS first, since it's much easier and cheaper to replace.