When you plugged it in to charge, did it actually show it was charging? If it didn't, then either the battery or the charger may need replacing. I would first test the charger on another device, or try another charger on your device, to see if that fixes the problem. If not, then you may well need to replace the battery.
The power button could also have been stuck when you plugged it in, so try plugging it in again.
If the tablet is still under warranty, you are best to contact your provider or the manufacturer and have them see about fixing it. However if it isn't under warranty, then you are free to (if you feel comfortable doing it) open up the device and see about replacing the battery yourself.