swap your cable out, try the monitor on another computer or try another monitor out on the original computer, does the issue repeat on the same computer?
Often times, the choke on the cord can be loose or has dislodged, and the color shifts will occur.
If it's random pixels, it's indeed a bad monitor or monitor element. If it's ALL of the green pixels on the monitor, I'd check the cord, but still wouldn't rule out a bad monitor. If you disconnect the monitor from that PC and the self test does it too, it's definitely the monitor.