white line stretched across the screen
The elastomeric connector at the edge of the screen has separated from the screen itself. If you apply very gentle twisting pressure to the screen you'll probably (but not necessarily) see a change in the white lines. That's why you were seeing a change in the lines when you opened and closed the laptop screen.
The reason you don't see the lines on a screen grab is because the video ram is working fine and has a complete and correct copy of what the computer wants to display, so that's what's turning up on the screen grab. The fault occurs at the very last physical connection between the computer and the display.
There are two options : You can replace the screen, or use an external display. The lines will not appear on an external screen for the reasons explained above.