I have replaced the battery but it won't charge?

This particular iPod is my nephews. From what I have been told it was powered off and placed on a dock charger over night. He returned the next evening and it wouldn't turn on. So his mother plugged it to a wall charger and still nothing. Won't charge or power up. I replaced the battery because they tell me it wouldn't hold a charge for very long before. Now I got it to power up, but it won't charge and powers off in less than 1 minute. Only did this a couple times and am sure it is the new battery needing a good charge to fully operate. The dock connector appears clean and in good condition from what I can see of it. Just wondered if it could be a bad dock connector. And if so has anyone ever replaced one of these. It looks like it will be incredibly difficult with 30 pins!!! And they are tiny. Thanx