it could just be a pixel problem, there are websites and programs that will throw as many colors as a monitor can handle, to kind'ov "refresh it" might work, might not, but its worth a try. you could also try to hit the refresh button on you monitor. if neither of these solutions work, then you have a bad monitor. i will try to find that web page or program i was talking about, dont have it on hand, that is unless someone posts it before me.
EDIT: I almost forgot, you could also change the resolution of the screen, if the green line moves with your changing screen size it is not your monitor, at that point it could even be a faulty video card, but my money is on the monitor.
EDIT, can you see your white mouse over the green line?