Does jiggling connections actually affect anything or are you searching for other solutions?
My first thought is the monitor may just be dead (though yours will be the first I've heard of).
In a few years, we're all going to be wishing for the good old days of CRT televisions. Flat panels are slick but right now, they don't last as long as a solid CRT design. We've had a fair number of flat-panel computer monitors die at work. I've also known people with flat-panel televisions that have already died. I don't think our Haas machines are going to be much different.