First thing you might try is to use another USB cable. Check the dock connector carefully for any bend, broken, corroded pins and debris. Clean it with isopropyl alcohol and a toothbrush, or similar tool. After that, try an AC charger. It is easily possible that your battery is at the end of its lifecycle. Replace the battery first, then re-evaluate and see what you have. Follow this guide for the repair and the battery is available right here. Hope this helps, good luck