New battery won't work unless plugged in

I recently bought and installed a new battery for my 5th gen 60GB iPod video. I followed iFixit directions, and the battery charged, albeit slowly. (I ended up using the 5V/1A little charger for my iPhone, because the original charger didn't seem to move the battery beyond the low-battery screen message.) After charging for the full course of the day, the iPod works beautifully when plugged in but immediately crashes/ turns off when I unplug it. Working on plugged in is an improvement over the old battery situation, where it simply wouldn't charge. But I want to be able to play it on the go, of course. When I click the iPod to light it up, I see the word "charged" and a battery icon with the plugged-in overlay. However, I never see any evidence of the lightning-bolt overlay that indicates that the battery is charging, even when I unplug the device for a while and then plug it back in. I've tried resetting the iPod, which works fine but seems to have no effect on the battery function. Is it likely that I received a dud battery, or might I have done something wrong? And where is the best place to pose this question vis à vis the product sellers (if I need a replacement battery)?