A restore of the device in iTunes usually rules out any possibility of a software glitch as it reloads the iPod with a fresh version of the iPod's software. One last thing you can try doing is letting the iPod's battery fully drain. Then charge it back up and restore in iTunes once more.
Otherwise, it's likely a hardware issue with the iPod's LCD display or its connection to the iPod's logic board. You'll need to pay to have your iPod serviced/replaced either by Apple or a third party repair service.
Here is Apple's pricing: http://www.apple.com/support/ipod/service/prices/