Okay, it turns out that it's any key on the keyboard, or any mouse move, to get the monitor to turn back on, after Doze has suspended, waited, and then resumed the system. The system resumes with the monitor black, Doze finishes its run, monitor still black. Then I press a key (including Shift) or I move the mouse and then the screen lights up.

This explains why it didn't induce that other problem... The other problem was also solved by keystrokes or mouse moves.

Anyway, I tried...
- Ghosting mouse moves to get the monitor to turn on. No dice.
- SendMessage(HWND_BROADCAST, WM_SYSCOMMAND , SC_MONITORPOWER , MONITOR_ON ); No dice.