This is a physical issue.
It could be something as simple as the LVDS connector with corrosion on it that needs cleaning or it's a possible there's cold solder joint or a failing component (possibly both). Only guessing (since I don't have the unit in front of me to test), I would say that it's the 12V power rail that supplies the display that's the source of the problem.
To further diagnose the problem, hook it up to an external monitor. If the problem doesn't manifest on the monitor, the issue has to do with the display and not the GPU.
You will need to take this in for service. If you have Apple Care, this should be covered. If not, you may have some luck with the Apple folks who may service it out of warranty.