The solution was very simple.
I have a Bluetooth mouse and a Bluetooth keyboard.
There is a setting that tells the Mac to not be activated by Bluetooth devices, but I'd rather not have to attach a non-Bluetooth mouse to the computer to activate the screen in the morning.
So if you're finding that you can't turn off the screen of the Mac, and have it stay off, try turning off your Bluetooth mouse if you have one.
And maybe Bluetooth mice should go to sleep and stay asleep if no one is moving them.
http://bit.ly/9Iy2iV