If pressure makes it go back to normal, it could be the cable that connects the monitor to the logic board is just loose. The other possibility is that cable got pinched in the bezel (which is a known problem) and is causing the cable to fail.
If it's out of warranty, you might as well check the cable. Just make sure you download a service manual.
Oh, and get a stack of little paper cups and label them. You're going to have about 50 screws by the time you get to the cable, and many of them are different sizes.