Are you sure it's a 4G iPod? This was normal behaviour for the 3G iPods.
The 3G iPod was the one with the four separate navigation buttons, rather than having them integrated into the scroll wheel.
While it's possible that something could be malfunctioning in the 4G iPod, I've never heard of this before, and generally if it won't take a charge it likely wouldn't sync either, since this basically happens on the same connection.
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