To rule out the charger cable, see if you can borrow one that's known to work from a friend (or check if yours is working on a friends iPod). If it still won't charge try to reconnect the battery (did you use the locking mechanism on the connector correctly?).
If that doesn't help, then three things come to mind as possible causes: the battery, the ribbon cable or the connector/logicboard.
It seems unlikely that the battery is the problem, but it can be examined using some kind of meter, that I don't know about. If the ribbon cable has been damaged, it's most likely to be where it's bend. But my guess is that if reconnecting the battery doesn't help, then something has caused malfunction either in the connector the logic board. As you changed the battery you could have touched a component or something else might have happened, that would cause corrosion leading to malfunction after some use.
It might be something that can be fixed by a cleaning. Or has something happened to your iPod, like a liquid spill?
good luck and please update on progress
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