iPod Touch WON'T reach full charge icon?

I bought my iPod Touch 5th Generation for $400 back in December, and it worked fine for the longes time. Around the time of the iOS 6.1.3 update, I began noticing radical changes in battery abilities. For example, it drains fairly quickly, and I have tried all the remedies suggested (i.e. turning the mail push off, WiFi off, brightness down, reboot, restart, and resetting), and nothing seems to be working. I have tried charging it for more than four hours, and yet no matter how long I charge it for, the fully charged battery icon will not appear in the battery symbol in the corner. Even more disturbing is the fact that it will go from it's maximum charge to completely drained within a matter of hours, whether it's turned off or not being used. People say take it to a genius bar at an Apple store, but there isn't one near me for hours. Should I just sell it and use the money towards a new iPod, or do you think it is the iOS 6.1.3 update, as I have read many complaints concerning its affect on the iPod battery? Thank you! 🙂