This sounds like a hardware problem for sure. So no, its not likely that a restore will do anything for your device.
If you have not dropped or damaged the device at all apple may replace it for free.
But it sounds as if the LCD screen has gone bad and needs to be replaced.
I'd check with apple first, and if they don't do it for free or cheap find someone reputable that will. Or do it yourself with an iFixit Guide!
[guide|67489]
Hope that helps!