Little but not real pulse

4th Gen iPod. What I thought was a simple battery issue I've come to believe is more the USB dock connection. I've replaced the battery. Same issue exists. The iPod runs out of juice. That's not to say this hasn't worked recently. But connecting it to computer needs constant wiggling of the dock connector. After that it seems it rarely remains connected. Does one replace that piece of the iPod? This was most likely damaged using a stand-alone speaker system which the iPod stood on.