As long as everything else is functioning correctly, it could be the power switch. If the power switch does not move all the way to the power on position then this can happen. It would be a good idea to clean it or replace it.
Getting a white screen after replacing the panel is common, and not a problem. Just soft reset your iPod by holding the power and home button, then once the apple logo shows up depress the power button and continue to hold the home button. Your device should then show on the display correctly. However if you do reset it, anything in its storage will be erased. If this does not work it could be a faulty panel.