Thanks for the tips but so far nothing has worked completely. However, I have discovered a new wrinkle. If the monitor remains ON, I open the Screensaver window and select the Power Management tab. If the shut down time is set to 10 minutes, I change it to 15 minutes and select OK to take me out of that window. Then I open the same window again and change the time back to 10 minutes. The monitor then shuts down after 10 minutes. I have also discovered that the problem seems to occur mainly after I reboot the computer. In otherwords, after a reboot, the monitor stays ON unless I go through the procedure that I outlined above. Then it works fine for quite some time. This must mean something to someone, but it doesn't make sense to me.