It sounds to me like the charging part is fine. Whether the battery will hold the charge is another question but at least the charging behaviour is as expected. The problem is turning the device on. Let's start with the obvious. You need a long press on the power button to turn it on. I am sure that's what you did but you did not say so. If that still does nothing, then the problem may be in the button. But all is not lost yet. You can make it start using the flasher. IIRC, the magic incantation is flasher -r.