Check if the receptacle moves on the circuit board or is lifted at all. It shouldn't.
Look at the small solder joints and tight space. I watched a video on micro-soldering and decided NOT to try it yet, despite many years building electronic kits and some repair work. A shop estimated $180 while replacement boards or iPods are $40-50.
Ensure the new plug is fully seated and inserted correctly. My new batter had to charge via wall adapter, not my computer, for over a day! Hopefully, you got the right battery for your iPod; mine was of higher capacity, but such a long charge cycle surprised me.
Also, read all you can and ask for expert help from the place that sold you the battery. I am not a pro at this, just a guy like you with an iPod problem or two. Four days, on and off, and finally mine is ok.