You can work through the remaining five 5 R's of troubleshooting.
It might also be a good idea to let the iPod's battery fully drain. Then charge it back up and restore it once more in iTunes.
Otherwise, it's likely a hardware issue with the iPod's LCD display, meaning you'll need to take or send your iPod in for service either via Apple or a third party repair service. Here is Apple's repair pricing.
Note that they don't actually repair the device, but exchange it for one of the same generation, model, and capacity. A third party service will actually replace the damaged/faulty part for a little less. Google "iPod screen repair" and you should get a number of results to work with.
I have done all the above, in fact it had no power, then I recharged it. Still a problem. So, I purchased a "new" LCD screen, and am taking to a repair service locally. Going to cost me less to do it this way, 15 for the screen and 30 for the repair. I think I might want to invest in an iPod Touch - the iPhone & iPad are spoiling me.