My issue is similar to the one that this user had, but was never completely resolved. There is another interesting fact about this problem that I didn't see mentioned there.

My iPod Classic has lines that go across the screen, but that disappear once the screen fades (not completely asleep). I squeezed different areas around the LCD as per one of the answers to the similar question, but nothing changed. The most odd part about this problem is that sometimes the lines extend along the width of the screen shorter or farther than others if I reset the iPod or after leaving it on the charger for a while.

Could this problem be a connection, a component on the logic board, or even the LCD itself? == Update ==

The lines magically disappeared. Not even joking. I didn't touch my iPod over the weekend, and when I grabbed it to go to the gym this morning, the lines were gone.