Chosen Solution
See video for details. It basically starts up with a bright white light and then turns into vertical lines. It also sometimes displays 5 lock screens vertically. I have already tried a soft reset, but it had no effect.
Do you still have the original screen in a somewhat working condition? If so, try the original screen and see if this problem persists. That way we can rule out the screen. Update (10/07/2018) @blewisgabriel Sounds like we have our problem solved! If you wish you can buy another replacement screen at the link below. Go ahead and mark this as correct for completion sake. iPhone 4S Screen
If you still have the original LCD screen, put it back in and see if it does the same thing. It might be a defective / bad 3rd party screen you have there, or it has been damaged. A similar sort of white to gray vignette and vertical lines problem happened to my LG Optimus L90 - that is, after I put it through some physical stress tests.
