If you have tried all of the suggestions mentioned under the appropriate section in this Apple support document, you may need to have your iPod serviced or replaced either by Apple or a third party service. It's a hardware issue with the iPod's LCD display.
Some users were able to resolve it by restoring the iPod numerous times and others corrected it by letting the battery fully drain and then charged it back up and restored it in iTunes.
If the Nano is still under Apple's 1 year warranty against manufacturing defects, Apple may swap it out for you at no cost if they don't conclude the issue to be the result of abuse or accidental damage. If you have an Apple Store nearby schedule an appointment with them and show them what you are experiencing.