Will not stay on unless the charger is plugged in
Your battery is failing.
Either replace the tablet (if still under warranty), or get a new one.
Save all that you can onto another computer, and move the stuff onto your new one. The Barnes and Noble items (ebooks and music) are saved under your account and password at the B&N site.
While it is possible to rip open the tablet to replace the battery, is not recommended. It is a difficult task that will damage the case.
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