Monitor not working

I have 2 flat screen monitors on my Mac Pro. They have been working side by side for several years. One is an Apple, the other a Benq. With no warning, when I booted up the computer this morning, the Apple monitor has a black screen. The little light at the lower right corner was slowly flashing. I first switched cables on the back of the computer to see if the graphics card had gone down, but the Benq just became the primary monitor with all of my icons and the Apple stayed black. The Mac still thought the monitor was working, however and opened files where I couldn't see them. Now I have unplugged the Apple monitor entirely, and Mac realizes that I only have one monitor. Is it possible that something has gone to sleep? The power and menu buttons on the side of the monitor do not seem to have any effect. With the monitor unplugged from the Mac, the little white light has evidently quit blinking.