I am assuming that you mean when you take it off the charger, it won't turn on. You didn't mention if it will turn on while attached to the charger?
Also, since this is an older device, it is quite possible that the battery is going/gone. So that even though you see the info on it 'charging' when it is plugged in, it actually isn't holding the charge.
First I would try seeing if it will turn on while plugged in. If it does, but turns off when you unplug it, the battery is the problem.
Now if it won't turn on even when plugged in, I would suggest you try holding down the power button for about 20-30 seconds and then seeing if it turns on. Both when plugged in and when not plugged in.
Also, make sure the power button (as well as any other buttons) are not 'stuck'. If they are, that will keep the device from working correctly.