iPod nano (2nd generation) won't charge

my iPod Nano (2nd generation) won't play. Screen has message that battery has no power and must connect to charge. When I attach to a charger, nothing changes and the iPod does not indicate that it is being charged.

Have tried toggling the switch on top -- nothing.

Have tried to shut down -- nothing. iPod is totally frozen.

Have tried two different cables; attached each to two different chargers; using several different power outlets. None of these combinations makes any difference.

Curiously, the little battery icon at the top indicates about a 50% charge.

Any suggestions?