What would cause the brake pedal to be hard and not go to the floor and still engage the brakes?

You could have a clogged brake line, most likely one of the front rubber ones.

The Brake booster might not be working correctly. Run the engine for a few moments, then turn the key off. Once the engine dies, press the brake pedal a few times. You should hear a hissing noise each time you press the pedal. Then hold the pedal down and start the engine. The pedal should move and get softer. If none of this occurs, verify that the booster has a vacuum source. If the booster has a vacuum source, and still does not boost the pedal effort, the booster is more than likely bad. One other alternative would be a bad check valve. Simply remove the valve and blow into it. It should blow easily in one direction, and not at all in the other.