A new issue with the 91' Corsica

Just finished the brakes system with minimal issues. The rotors and pads are like new but sat for 2 years while the car was not driven. I replaced all the brake lines and cleaned all the components. The calipers, wheel cylinders, and components work perfectly fine. I followed bleeding procedures exactly (minus tapping the calipers with a dead blow hammer or rubber mallet cuz I don't have one yet) and yet my brakes still don't act the way I believe they should. They work as far as stopping the car. I should be able to lock up the tires when I press firmly, but no matter how hard I press they don't lock. The brake pedal goes almost to the floor, but no matter how hard I press it will not. I have bled them 4 times now thinking there might have been air still in the lines but after the second time there is no air in them. It is hard to explain exactly what it feels like but they are almost spongy but not in the way that air in the lines would cause them to feel like. Any suggestions or comments would be greatly appreciated.
Thanks

If you have anti lock brakes it will not lock up. Not sure about that year having them. Do you feel a bit of a pulse?

My car does not have anti lock brakes. However I have fixxed the problem I took a deadblow hammer to the calipers and wheel cylinders and got a bit of air to come out of them and they are working fine now. Thank you for the reply.