2000 Cadillac DTS Won't start

I have a 2000 DTS, when I turn the key I hear a rapid clicking sound and the car wont start. I've tried to reset the alarm with the remote and by locking and unlocking the doors with the key. I also unhooked the battery to see if that would help. When the car was running it somtimes would cut out while driving, I would have to restart the car to get it going again. All the lights on the dash and all the headlights are working, I don't know what the problem is, can I get some help please, please, please. I'm loosing my mind.