Battery went dead overnight, found a plug under the dash that was making a rattling noise...

Car battery must have gone dead, car won't start even when jumped. I used a 12v tester just to see if there was any power in the battery and there is some. There was a strange clicking under dash and I found it to be a black electrical plug that was plugged into a black box that didn't seem to go anywhere. I'm not sure what the plug, or the black box is for. Any help on what it is or what the problem might be would be great. Thanks!