This may or may not be what you mean by "goes green" but I've noticed that when DVI cables go bad it often results in green noise all over the screen. My office

This may or may not be what you mean by "goes green" but I've noticed that when DVI cables go bad it often results in green noise all over the screen. My office had a mix of both HDMI and DVI adapters for their macbooks, and I only ever saw it with DVI, but either way it might be worth swapping cables and seeing if the problem isn't with your macbook.