Brand New iPod won't hold a charge

Just opened it up 2 days ago. Plugged in to AC power to charge and it booted right up. Left it charging overnight but when I disconnect it flashes Low Battery - Connect to Power. Connected it to my computer to see if it would sync. It did. Dumped all my audio, videos, pictures, etc. But if I disconnect it from the computer it immediately flashes Low Battery - Connect to Power. I've reset it to factory and that didn't help. Did I get a clunker ? Do I return to the place of purchase or go to an Apple store?