Thanks for the question. The following article outlines troubleshooting information for iPod nano. While it mostly refers to the 6th generation, most steps apply for your model as well:
Will not turn on or screen remains dark
- Connect iPod to power for at least ten minutes to ensure that the battery has enough charge to allow iPod to turn on.
- If iPod does not turn on after ten minutes, try resetting the device while it is still connected to power. Reset the iPod by holding down the Sleep/Wake button and the Volume Down button for at least eight seconds or until you see the Apple logo appear.
- If the Apple logo appears on the display, connect iPod to a computer and verify that it appears in iTunes and can play music. If iPod appears in iTunes and can play music, no further troubleshooting is needed.
- If the screen remains dark and will not turn on, then your iPod may need service.