I can press the brake pedal and I get a hard pedal that stays. When I start the car the pedal will go to the floor.

Is this the Brake Booster ?

 

Oh, it's a 1500 LT 4wd

 

I would say a failing master cylinder,the booster is just to assist, so with the assist,you can push easier,and further cause of a weak master,one test for a booster is after shutting off,you should have 1 more easy push on pedal,that's the reserve vacuum