Article: TS3474 iPod nano (6th generation): Hardware troubleshooting may help you with your white screen. Take a look in the displays section for white screen.
Display shows a white screen
Try putting the iPod into disk mode:
Reset the device (press the Sleep and Volume Down buttons simultaneously until the display turns black—about eight seconds).
When the display turns black, hold down the Volume Down and Volume Up buttons simultaneously until the device enters Disk mode.
While the device is in disk mode, sync it to iTunes and try to restore.
Hope this helps,