1987 Chrysler 5th Avenue weird problem

My car won't start and won't even turn over. We tried jumping it and it would turn over a little bit, but not strong at all. We popped in a new battery and still the same problem. The new battery won't turn over at all unless you jump it and then it will turn over just a little bit. When not jumping the car, you can hear just about 3 small clicks wen you try to start it. When you turn the key to the off posistion and then try to start it again it is absolutelly dead unless you take the key out and put it back in again and then you hear the 3 clicks again. The alternator indicator light is on D also. Any idea what in the world is causing this? Thank you for any help in advance.

Ryan