Welcome to iMore! Try performing a soft reset. To perform a soft reset, hold both the power button and home button down until you see the Apple boot logo. If that doesn't work try charging it using a different cable and power adapter, just to weed out an issue with the cable or adapter itself.
The unfortunate truth is that your device might just be showing its age at this point. The battery is often the first thing to go in an aging device. Hopefully it's actually an easy fix though!