miataguy

I just had this happen to my yesterday and today. Yesterday when I started my car, I heard something click about 10 times per second. I tried starting it again, hear the clicking, then the battery goes dead. I had to get someone to jump start the car for me. This morning it started just fine. I then tried starting up the car about 15 min ago, and I hear the same clicking, so I wait about 5 min then start the car and it starts right up. Could this be the starter going bad, or maybe the alternator?(or both?). I do hear a screetching sometimes when i start the car or when giving it gas while driving.