Chain saw, it could be that a new display fixed the issue, without the person who asked the question coming back to mark the solution as accepted.
If your iPhone was never opened before, I advise you to try a new known good display to see if it fixes the issue, like con says here above. Best would be if you could borrow one from another phone for your trial. You can use [guide|10588|this guide] to attempt the repair.
If it doesn't work, let us know so that we may discuss other issues that could be causing it.