Quite often cameras have the light meter just check a spot in the center of your view. In the picture you posted the center of the shot is NOT the brightest part of the picture. You camera is properly exposing for the front of the iPod and the lit screen which is not being metered is over exposed.
The suggestions of pouring on lots of light in the room is a good one, as is turning down the brightness on your iPod. On my 3rd gen nano you go to the main menu -> settings -> brightness.
You could also zoom back, but the screen in the center of the shot, and then crop in your computer.
Good luck
So, any follow up? Did you get a good photo?