If you have not already, first try a Reset (restart) on the iPod
Learn how to reset your iPod - Apple Support
The backlight may be faulty, either OFF all the time or not bright enough. If the screen is difficult to read in normal room light, it is probably not an "original" iPod, since the earliest iPods have a monochrome screen that is easy to read in ambient light (with or without the backlight). So it has a color screen? Here's a list of all iPod models, if you'd like to identify it precisely
http://www.everymac.com/systems/apple/ipod/index-ipod-specs.html
Since you already tried adjusting the settings for backlight, try the Reset All Settings command (it may be called Reset Settings). It should be at the bottom of the iPod's (onboard) Settings screen. This resets the iPod's internal settings to default, including the settings for backlight. Then try adjusting the backlight settings again.
If that does not help, you can try doing a Restore on the iPod using iTunes.
NOTE: If your iPod is 4th gen (like "iPod Photo"), you may need the USB power adapter that came with it or another Apple power adapter (like one from iPhone or iPad) to complete the Restore process. Third-party power adapters often do not work for this purpose.
The Restore button is on the iPod's settings screen in iTunes. This erases the iPod, reinstalls its software, and sets it default settings.
Use iTunes on your Mac or PC to restore your iPhone, iPad, or iPod to factory settings - Apple Support
If the Restore does not resolve the problem, the cause is likely to be related to a hardware problem on the iPod.