iPod Touch 4th Generation BATTERY / CONNECTIVITY. Help?

Hi, two weeks ago I got a 4th Generation, 32gb iPod Touch. I charged the battery for an entire day before I used the iPod and all was well for about three days. Now my iPod is connected to the computer and will not turn on. My iPod will not work unless plugged into the wall charger and even then it says the battery is 100%, however, as soon as I unplug the iPod it turns off. I don't want to lose all the things I bought from iTunes or my apps. So, what should I do? It won't turn on at all.