Lights dim system shuts down no electrical?

I have a 2001 chevy cavalier the engine is 2.2 and recently while I was drivng my headlights went dim along with everything else inside the door, the guages shut off and went back to zero while I was still driving, and where my mileage is at said "error" the farther I drove the dimmer everything got until everything started shutting down and my car stalled, I thought it sounded like and alternator problem but I put a new alternator in and the problem still occurs, its getting more frequent each day