My battery life isn't lasting more than 2 songs, help?!

I got given a refurbished Ipod 5th gen in april.. Since then I have had a a lot of dificulty with the battery life.. I have updated the system, reset it numerous times, reinstalled it, restored it and it still has the same problem. I'm at my whitts end. My old Ipod nano lasted me years an the batter life lasted days longer. Just before it runs out I can feel something inside it (like a motor) buzzing then fizzles out and turns off, even when I have charged it for the recommended time on a new ac wall adapter.

Any suggestions?