As I understand your post, you can see the music when the iPod is plugged in to the cradle and is being fed power from the USB/Firewire connection BUT you cannot see the music when the iPod is not connected to anything. Is this correct?
Assuming yes, do you see anything at all on the screen?
If the answer to that is NO, and you have followed all the troubleshooting tips in the manual, including the resetting option, then I would suggest that you may have a defective battery. When attached to the cradle, the iPod draws power to charge the internal battery and to run itself. It obviously does this. Without external power, it doesn't work. If all else has failed, take it back and get it replaced under warranty.

Hope this helps