4th Generation iPod won't hold a charge

I bought a brand new 4th Generation iPod for my wife to replace her 2nd generation one. The problem is, outside of it being docked on the iHome mechanism or being hooked directly to the computer via USB cable, it won't respond if unattached. It's simply a black screen. I can't get it to reset or do anything. It seems as if the battery is not holding a charge, or is there some other nefarious thing going on?

Anyone else had this problem?