If turning it off and on doesn't fix it, then its a replacement screen I would think.
You could take it to Apple to a diagnostic on it, and then give you the verdict. If its the screen, get it replaced, and I would use Apple then. Here in Aust, we have that many little booths in the Malls, and Shopping Centres that charge $75 or there about for a screen replacement, and because of this, Apple here has moved to their prices, or close enough too.
Apart from that, there isn't too much more you can do.