I know this is about a year old, but my 5Gen 30 GB iPod started doing this. It's out of warranty and, who knows...the way Apple has hardware turnover, there may not be any parts for it.
I'm reluctant to buy a new one because this was a Father's Day gift and has an inscription from my sons.
Does anyone know of any tricks I an try? I tried putting it to sleep (with the play button, not "the needle") and reset (menu + center). Every once in a while the screen will return to normal, but that is becoming more rare each day.
Other than the white screen problem, the thing works fine.