I got a acer aspire one netbook as a gift, it will not turn on unless the charger is plugged in, even if is turned on and i remove the power cable, it turns off.
If it is a new one, ask the person who gave it to you for the receipt and take it back under Warranty. Does it start on mains electric power if you take the battery out?
So dead that it can't even pass power through itself. It probably lay unused for some time. Beware the really cheap Chinese copies if you buy a replacement on e-Bay.