Angela you might want to try this first:
Toggled the hold button on-then back off
Reset the iPod by holding menu-select for at least 10 seconds and follow the iTunes instructions.
Restore the iPod using iTunes.
I had the ipod White screen of death too, and I tried everything to try to fix it, including restoring, resetting, etc. but I finally got the screen to work by going to the diagnostic menu and running through some of the tests there. Info for diagnostic is here http://www.internet-tools.co.uk/blog/index.php/2008/01/30/ipod-nano-3rd-generation-diagnostics/
Then I reset the ipod in the diagnostic menu. Sometimes this helps for a short while. I do not exactly know why this reset is different than the one that you initiate with the click wheel, but it is.
From my experience this problem is either related to a loose ribbon cable, defective screen as well as possible moisture. I have seen some display cables that showed signs of corrosion and so did the connectors without ever having been submerged.90% of the time your problems are a hardware issue and its usually related to the screen. I believe the main issue to be a faulty connection with the screen contacts. Hope this helps even so it is not good news...good luck