Try flexing the LCD corners a little some time the frame gets a little bent happens at edge of the screen .
But could also be a video chipset or cheap nice card issue. But sounds more like the frame for the LCD slightly bent or pinched near the edge the line appears had to fix those issues before can also be the plug for the LCD screen needs reseated if still having issues
Exactly it can be just need apply enough force but not to much force edge of screen getting pinched more likely cause the frame partially bent if line dissappeared don't worry about it till it comes back.if it does try flexing it one way or the other with enough force on both corners fixed plenty of em that way
cable not easy to get to usually access it under they key board normally ,a strip at the top of the keyboard got to pop off that runs across the top of the key board covering the screws. that's the only way to get to the monitor cable without taking whole thing apart and yet some time sen the cable cuase thew issue ya was having if aint that is video going bad or screen slightly bent like I said before cant really be anything else.