I would agree with all the solitions above. Always try the reset , re-seating lcd connector options first.... And of course if you swap the screen and a new one works then of course you know the first screen was faulty.
IF ALL of those things fail and you know the screen itself is not faulty then one thing that worked for me was:
Using a magnifer (20x binocular if possible) look at the area to the right of the lcd connector on the mother board - with the lcd itself disconnected. There should be a row of tiny components in a vertical line between the right hand side of the connector and the ambient light sensor (the one with the foam sponge around it). The 2nd component up should be a little black resistor. I had accidentally knocked mine off whilst prying up the lcd connector.
I bridged that missing resistor by applying some solder across the 2 pads and when then lcd was re-connected the white screen was fixed. That was a year ago & the ipod has worked fine since. Ideally you would get a resistor the same size & resistance , but I didnt have access to smd reworking-type equipment. So far so good!
You definitely need that magnifier-preferably stand mounted so you have 2 hands free to do the soldering underneath.