I am also new to the forum and to posting. I, too, cannot figure out when my wireless keyboard is "on" or "off." My iMac is 3 weeks old (I bought it three weeks ago) and I already just changed my first set of three batteries. Maybe the batteries that came with the keyboard were bad? Anyway, here is what I have learned:
Bluetooth works both ways; you CANNOT turn off the keyboard while the computer is running. I have tried. The green light in the upper right corner lights up, then goes off, but the keyboard still works. Somehow the connection via bluetooth is still connected even while trying to shut off the keyboard hoping for "connection lost" message. It won't happen. Therefore, try this:
To turn off the computer, mouse, and keyboard:
(1) Go the the Apple icon in the upper left-hand corner of the menu bar, and click on "shut down". A box will open up telling you the computer will shut down in 60 seconds unless you click the button. Click it, and let the computer do its routine shutdown proceedures.
(2) After the screen goes dark:
(a) Turn off the mouse. That part is easy -- just a sliding switch on the bottom.
(b) Turn off the keyboard. Press the button on the top right side once, and the green light will come on. Because the computer is now off, so is the "bluetooth" so now nothing is "talking" to the keyboard so the keyboard will shut off. Wait a few seconds after that, and press the "Caps Lock." The green "Caps Lock Status Light" will NOT come on. Why? The keyboard is OFF!
Now, to turn the computer on, follow these steps:
(1) Turn the mouse on.
(2) Turn on the keyboard by pressing the button once. The green light on the top right will momentarily turn on, then shut off. DON'T PRESS THE "CAPS LOCK" BUTTON TO TEST WHETHER OR NOT THE KEYBOARD IS ON!!! Why? Since the computer was not turned on yet, the "bluetooth" is not activated yet, and the keyboard doesn't know what to do.
(3) Turn on the computer. As it goes through its start-up procedure (booting up), bluetooth will turn on and sync the mouse and keyboard with the computer. Now when the computer is ready for action, type anything and the keyboard will work! Press the "Caps Lock" button, and the green light will come on! Now, with bluetooth running, the keyboard and "Caps Lock" know what to do.
Summary: To turn off the computer, turn it off, and after it is off, turn off the mouse and keyboard.
To turn on the computer, turn on the mouse, turn on the keyboard (but don't hit any other key yet), then turn on the computer. Once the computer is up and running, so is the mouse and keyboard.
This has been my experience, and I hope it helps you. Good luck!