iPod Ipod Won't Charge

I just bought and Ipod Nano. Got it home and when I turned it on there was a little battery life. After a few minutes the thing died. Plugged it into the computer to charge, and the screen is totally blank. It's like it won't even turn on. Went back to the store and bought a usb Power Adapter and the same thing happened - Nothing on the screen. Read somewhere that all Ipod's come with a Cd with the software. I did not get any CD with mine.

Any suggestions?