2002 Chevy Cavalier Battery light

My battery light will not go off. It did not come on until my radio went out and continues to make a popping/static noise when I brake, put the key in the ignition, or open the door. The door and key in the ignition chime is faint. The time and station show on the radio but it still does not work. Fuses have been checked altanator has been checked and even with new battery light will not go off and radio will not work.