This is a tricky one! Did you get your system wet at some point or have some liquid spillage into the keyboard?
The Air’s use the graphics engine of the CPU and as we can see the displays image is present so we know the CPU & graphics engine of the chip is working. Yet the crosss hatch (H&V) implies a logic board signal issue.
Are you really pressing on the display its self or just pressing on the brightness button?
At this point I think you’ll need to plug in an external display to see if the image is clean on it. If it is thats points to the internal display needing replacing if not then that points to the logic board has issues.