Let the master cylinder run dry and now the brake pedal goes to the floor when I turn the car on. Is air still in the system?

I pulled the car out of storage and i noteced the left front caliper was leaking so I replaced the caliper. The only problem was the master cylinder ran dry. I bleed the brakes three times. I did not see any air in the lines after I bleed them a third time. When the car is off the brake pedal gets rock hard when the pedal ia depressed about half way. With the car on the brake pedal goes to the floor. Would this be cause by air in the system? The car is a 03 ford focus.

"Would this be cause by air in the system?"

Yes it would.

Yes, you need to bleed all four wheels starting with the one farthest from the MC, the right rear, and ending with the left front.

If the pedal goes down, you either have 1.air in the system, 2.another leak (you would notice brake fluid all over), or 3. The master cylinder is bad (not likely if the pedal gets rock hard when depressed with the engine off)

Air IS in the system. Make sure you bleed the master cylinder too.

If the pedal bleeds up nice and hard stays hard until you start the engine then goes spongy Id be looking at the vacuum booster I once bleed 4 litres of brake fluid thru a system until I worked out the booster was the problem

Try cracking open the bleeder furthest from the master and let it gravity bleed for a half hour, close it, then do the same to the next furthest and so on.