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I just replaced the battery with an iFixit (super easy!) and the iPod started right up. It is showing little to no battery power. When I connect it to by Macbook, iTunes recognizes it, but it does not charge. I’ve tried multiple chargers with the 30-pin cable (brand new) and I can’t get the lightning bolt to come up. The only suggestions I’ve seen are related to replacing the battery, which is what I just did. I went back, disconnected the (new) battery and reinstalled it, still the same issue.
Your problem is the connection. The iPod 3rd Gen does not charge through USB but needs Firewire connection. This model only syncs through USB. Hope this helps, good luck.
You need a FireWire cable and power adapter to charge it. Cable: https://www.ebay.com/sch/i.html?_from=R4… Power adapter: https://www.ebay.com/sch/i.html?_from=R4… Note: Some eBay listings already include both things in them, since they are used together.