Generally a green tinted screen is a result of a poor video connection to the monitor. Try unplugging and replugging each end of the video cable and while you are at it, examine the contacts for signs of corrosion or dust. The unplug/replug will usually clean any crud off of the connectors. If that fails try another video cable. Connections inside the cable at either connector can get broken or damaged. If that is the case replacing the cable is easier and probably cheaper than attempting to repair it. If you still have a green tint the video card in you Mac mini or its connection to the logic board could be at fault and in that case a trip to the Genius Desk at the nearest Apple store is warranted. (Be sure to go online or call ahead and make a Genius Desk reservation before you go. That can save hours of time waiting for them to "work you in" to an already jam packed day.