I have a 2010 MacBook Air with a black horizontal line across the screen. as shown in the photo below. I don't know when it started; I just remember that I opened the lid today and saw it with the stripe.
As far as I know, it's not a GPU issue because connecting it to an external display does not show the problem. I've tried plugging and unplugging the display cable (no results), so I'm not sure if there's anything else I can do before I consider buying an used screen.