Why do my batteries only last a few seconds?

This camera has worked fine for a few years, but recently the batteries have been dying very quickly - the low battery sign flashes, then the screen goes blank and when I turn the camera on again, either the screen says "change batteries" or turns off in about a second. When I get lucky, the camera will stay on just long enough for me to snap a picture. After changing the batteries, they usually don't last more than a minute. I've tried the toothpick trick with folded pieces of plastic straws but it doesn't help.

I may have dropped the camera or dropped something on it, because there is a small crack on the top corner, next to the shoot button. Could that have caused this problem? Any suggestions are much appreciated.