My ipod touch seems to be broken?

I bought an ipod touch for christmas and its been working fine up until a few days ago. It started to not turn on via the home or unlock on, and i had to plug it into the computer to see the unlock screen, after which it worked fine. Now when i plug it in nothing happens, but i can still hear the chime (plug it in with volume and you'll see what i mean). It has got battery, but im not sure whats wrong with it. Can anyone help me? P.S its an english 2nd gen touch if that's of use to anyone