Why is your ipod nano sixth gen backlight randomly not working?

The backlight on the 6th gen iPod nano is known to be moisture sensitive. Rain, or even sweat, may enter the body of the iPod and corrode the contacts that connect the display assembly to the main board.

Replacement of the screen may work although in most cases this is due to the connectors being scraped clean of corrosion. Same effect might be had by just reseating the original display assembly.

To get rid of moisture put the iPod in a sealed container with a couple of packets of Silicagel (or dry kitty-litter). Or put it in a warm (not hot) dry place for a couple of days.