Lebon14, is the monitor a CRT or LCD? If CRT it is probably the monitor, LCD could be the monitor, however, it sounds like the video card. If the system is powered down for a time (long/short) does the monitor come back on for that 10 to 15 minutes before the monitor goes green again.
Realize there are a lot of questions to answer, however, more information is needed to determine the problem. Will do a search to see if anyone else is having this problem.
Google has a ton of information on this and other screen issues. So without the make and model of the monitor it would be difficult to determine the problem.
Edited by Lee 10/2/09 @ 2100