usually they will only come on via a computer once they get toally discharged. mains chargers will not work as they sometimes need to detact a small voltage from the unit to start the charge. If its dead flat they won't charge it.
I am talking from my own experience. I had a dead Nano and it would not charge from a PSU or dock, but did from a computer. Possibly it was because it was not an Apple psu. I would advise anyone with a dead Nano to try recharging from all sources.