It is probably not dead, just discharged. Plug it in and charge it overnight.

Android is bad about allowing apps to stay active even when you think they are closed and even when the Fire is supposedly asleep. Some apps will periodically awaken the Fire and try to phone home so-to-speak to acquire data. If the WiFi is on it will phone home, if the WiFi is off it will still try to phone home. This can easily cause the Fire to discharge the battery even when supposedly asleep.