Car will not start, rapid clicking sound

My fiance's car was not starting two days ago. I put in a new battery, and when I started it, it was working. Just today, on the way to the store, the ABS light came on, but the car didn't shut off. The radio was turning on and off. When she stopped and shut down the car, and tried turning it back on, it would not start. All she hears is a really fast clicking noise when she tries to start it.