Is the Backlight Timer setting on the iPod's Settings screen set to OFF?
If it is NOT set to OFF, you can try the Reset All Settings command. It is the last choice on the iPod's Settings screen. This sets all iPod settings to their default settings. If your iPod has a black and white screen, the default Backlight Timer setting may be OFF, so go back to that setting again and make sure it is set to a choice that is not OFF.
If the backlight still does not come on, please post back.