My iPod touch 4th gen wont charge or stay on

My Ipod was working fine then all of the sudden it would not turn on. So I plugged it into the charger, it turned on, saw it said that it had a half charge. But as soon as I unplugged from the charger it would turn off and I could not turn it back on when it was unplugged. Now I think the battery is dead, it wont charge and when I plug it in now I only get the screen with the usb cord pointing toward the iTunes sign. any thoughts?? might be shot......