iPod Horizontal Lines On iPod Classic Screen

I am wondering where I should start with my iPod Classic. I just got off the phone and as it turns out I am two weeks out of warranty. I knew I was cutting it close but I just didn't have the funds at the time to purchase AppleCare. So...now I am looking to fix whatever happens to be wrong with my iPod Classic. I turned it on this morning and noticed there was a black horizontal line going across the screen. The line appears to be one pixel thick. It isn't really an issue as I don't watch videos on my iPod, seems to just be bothersome. Where would you guys begin? Should I start with replacing the screen?

Thanks for your help, guess I should have just bought AppleCare when I bought it.

Yeah, it functions properly. I am just afraid this is the start of the screen going out and I would like to fix it now before the problem gets worse. I feel fairly confident in replacing the screen as I have opened up an iPod video that was given to me in an attempt to repair water damage. Either way, I just thought I would ask to see if anyone else has had issues with this so I had an idea of where to begin.