iPod in a constant state of charging, post-battery replacement.
I recently cracked the screen on my 30 gig iPod Video, and decided that it was time to swap out the slowly dying battery while I was in there.
Sounds like a faulty battery (I doubt its a logic board issue as it can hold a charge at least), I'd contact iFixit about getting a return/replacement.
iPods do not correctly report the charge status of batteries with mAh ratings > stock.
I had this problem too, post replacement battery, i tought i cracked something that might be the problem.