Can anything else be done to fix the white screen on a 3G besides restore/upgrade and DFU/restore?
If everything but the display works, you can try adjusting your display cabling and/or replacing the display unit. On that model, the digitizer is not tightly coupled to the display, so you can get a piece on ifixit. I remember once breaking the display on my third gen nano. It went white. Probably a defective display, but nothing that can't be replaced. 

Before messing with it, I'd definitely give it a shot at the Genius Bar, if you're local to one. They have diagnostic tools and such.