When I click Turn Off Computer, it goes into what I guess is hibernation. A tiny light on my monitor changes from green to amber. Is this off, or what?
No, your computer has powered down, just like it should.
Here’s what’s really happening: You’re shutting off the PC, but there’s still power going to the monitor, which is still on. The monitor isn’t receiving any imput from the PC about what to display, so it turns off the screen. Some older monitors don’t have this power saving function and display a blue screen or some other color when they aren’t receiving imput. Some even show the color stripes like televisions once did after the station quit for the night!
Look at your other pieces of peripheral hardware. Most optical mice, printers, scanners, and even some keyboards have an indicator light that they are powered and/or on.