Ipod Nano won't charge or show in itunes

I bought a used nano, either 1st or 2nd generation, not sure. The usb charger that I use for iphone and ipod classic seems to work; it provides power to the nano. But the nano will not charge (batter dead?) and it does not show in itunes. I've gone through all the trouble-shooting steps, including putting it into disk mode, but it still will not show in itunes. Is it just dead or is there something I can do? I paid 50 cents at a garage sale so can't go too far wrong but it would be nice if I could get it to work. Thanks!