2nd Generation iPod Nano Dead?

My 2nd generation iPod Nano was working fine this morning. Played music as it did for all these years. Later this afternoon I turned it on and the display would not light up. No music played. Seems like the battery is totally drained. Plugged into USB wall charger (from Apple) and get no indication whethr or not this thing is charging. Same when I plugged into my Mac. Does not show up in iTunes or on the desktop.

Is my iPod Nano Dead? Has the battery bitten the dust and cannot be recharged again? It's a shame that none of these iPods have user replaceable batteries... Other than being dead I am quite sure that if I could put in a new battery it would work again. I don't like spending a lot of money for something that does not last me at least 10 years.