Typically, that clicking noise will mean a dead battery. But that assumes a few things that you might want to investigate:
1. Make sure all of your connections are solid. The big positive wire from the battery goes right down to the starter. Make sure it is tight at both ends. Check for corrosion and clean up connections with a wire brush. Make sure your negative goes to the engine block (or frame) and is solid at both ends. There should be at least one ground strap going from the engine block to the chassis frame or firewall. That needs to be tight.
2. That connection game also works for the jumper cables when you try to jump it. They have to be tight. Usually I pull the handles apart as I twist them around the battery post - make the teeth dig in good. And allow lots of time for the battery to charge up. Make sure the lights and crap are off so the battery charges faster.
3. If all that is ok I'd say the solenoid or starter motor would be suspect. An old-timer trick that still works sometimes is to hit the starter with a hammer (not too hard) to try to free up the solenoid or get the starter motor out of its dead spot. If that is your problem, replace the solenoid or starter. Usually they are the same part. On a Cavalier the starter will be on the front of the engine in the middle, all the way at the bottom - just inches from the bottom of the radiator.
4. There is also a small chance that the battery is so dead it will not take a charge, but I am guessing that it was fine one day and didn't start the next. If the car has been sitting for a couple months, you may need a new battery. A shop will be able to test it for you. They don't just use a volt meter, but a higher-tech tool that measures the capacity, like a Micro 490 or equivalent.
Try all that stuff. 99% chance you'll find the problem.
Friday, April 27th, 2007 AT 4:44 PM