I doubt it's a software issue, but just to be safe, first restore the iPod through iTunes.

After that, try replacing the display.

If that doesn't solve the problem, all signs point to logic board, unfortunately.

Apple seems to have a "white screen problem" with at least some iPods.

It was found at different models (touch, nano, ...) yet.

<http://www.ifixit.com/Answers/View/11870...>.

Mine is a 2.Gen iPod nano.

As far a I understood it looks like a problem with electric isolation between the circuits and the housing.

Before ordering and installing spare parts try to run your device without housing.

Would be cool to hear if that works for you.

I have fixed the white screen problem multiple times (both with nano 2nd Gen and 4th Gen models) by removing the battery and leaving the iPod battery-less for a couple of minutes. Although the white screen problem is frequently a problem with the display, sometimes it seems to be a problem with the mainboard getting into a state it can't get out of unless power is removed completely. A hard reset using the clickwheel (menu and enter pressed at the same time) doesn't do the trick in those cases.