Welcome to Apple Support Communities, and thanks for the question. I found the following documentation on what to do if only an Apple logo appears when you turn your iPod nano on:
If this happens, the iPod software may have been damaged. Put iPod into Disk Mode, then restore or update iPod's software.
- Put iPod into Disk Mode.
- iPod should appear in the iTunes Source pane and on the desktop or in a Finder window, or in the My Computer window.
- If a message appears that says the volume could not be mounted and asks if you want to initialize the disk, choose to initialize iPod's disk. Use Mac OS Extended format (HFS Plus) if you have a Mac, or FAT32 if you have a Windows PC.
Warning: This process cannot be undone. All of your songs, videos, and other files will be deleted. Always make a backup of your important data.
- Follow the steps to update or restore iPod. If you manually put iPod into Disk Mode it may need to be reset before you can use it.
- If you cannot put iPod into Disk Mode after performing these steps, it may need to be repaired. You can arrange for repair at the iPod Service Website.
All the best,