One solution that I found for the iPod Touch when you encounter the white screen of death. If your iPod is frozen, then follow these simple steps and you’ll be back up and running in no time. It requires what is known as a system reboot.
step-1 Locate the power button. This is the rectangular button on the top left side of the iPod Touch.
step-2 Locate the home button. This is the circular button on the face (screen) of your iPod towards the bottom.
step-3Hold the home button and the power button at the same time and wait until the device shows the Apple logo on your screen (should take around 30 seconds). Your iPod should reboot with your files just the way you left them.
step-4 If the hard reboot doesn’t solve your problem then connect your iPod to iTunes. iTunes should detect a problem with your iPod and give you an option to restore it to factory settings (erases all your songs and files so back them up first). Here is a video for the same.
You can most certainly open the iPod and make sure that all connectors are properly seated and no obvious damage is on the inside.
Now if it continues with a blank white screen and won't respond to any of these steps than it's most likely a hardware related problem, and related to the LCD. Replace the LCD and it should do the trick, best of luck to you.....