That sounds a lot like the "White Screen of Death" :) Try to make a hard reset
press and hold the menu and select button until the apple logo appears, that way it should work again.
If that does not work you can always try this. Apple suggests that you ensure your iPod is charged before following the next step. How exactly you check a charge on an iPod screen that is completely white has yet to be revealed. But hey, give it a shot anyway. Plug the iPod into a high-powered USB port, let it sit for 2 hours, then disconnect it. If you have a wall charger, plug in the iPod, then follow these steps while it is still plugged in.
1. Turn the Hold switch on, then back to off.
2. Press and hold the Menu and Select buttons until the Apple logo appears
3. Immediately switch your figures to press and hold the Select and the Play/Pause buttons until "Disk Mode" appears at the top.
For a lot of people, this solves the problem. Connect the iPod to the computer and (assuming it shows up) reset the iPod again to get it out of Disk Mode. If at this point you still have the white screen, restore the iPod using the restore function in iTunes under the Summary tab (this will erase everything on the iPod and put it at factory settings).
Don't disconnect or eject the iPod until the store is totally done. After you think it's done, wait another five minutes.
Or is it possible that there is something on the screen but you can not see it, sort of. Shine a red light across your display and see if you see the menus dimly. If so then I would suspect suspect that your backlight is out. I do not think that it is easily fixable but may require a new logic board. Of course all of this does only hold true if you made sure that your display was installed properly and all connections are tight etc.. Good Luck and let us know