I work at a cellular repair store and have come across this issue multiple times. To fix this issue the first time I encountered it I simply bridged the internal charging dock with the third solder point on the right using a metal dental tool with a rubber handle. This fixed a dead iPod that BEFORE revived would only give a white screen and no iTunes response.
The second time I encountered the white screen I took the combo off multiple times and thought it wasn't plugged in correctly but that didn't fix it. When plugging it into iTunes I got a response from it and made a backup of the data. By restoring the iPod from the backup with "encrypt local backup" option pressed (this option saves passwords/account information so you don't have to re-enter all of your passwords after restoring) and once it was restored the screen came back to life.