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If you can mess with hardware, a little "clear" nail polish on some of the connectors for video/ram can do amazing things (I've actually been told by a student that the motherboard was dead when in fact it was the video and cache being "toast"). You can safely remove the nail polish with a non-acetone nail polish remover.
Nail polish is tricky enough but not an actual field problem. A field problem would be, take a separate video cable (for monitors that aren't permanently attached to a cable), find a pair of needle nose pliers and twist around and pull out only ONE video pin on one end only. Put the cable on the monitor and turn the computer off. Let them boot it up and troubleshoot. It simulates a defective cable. But make them find the cause. Most people won't notice the single missing pin.