[NoRedTape]

"Now here is the thing - my big monitor is now AWAKE but the laptop screen apparently has now gone to sleep!!!"

--I would try the "ALT key + F8" combo (hold down ALT and tap F8) until both monitors come on again at the same time. They will rotate one off, one on until both illuminate. (this is the method to use for a projector, too).

[Freedom'sWorthIt]

That did not work.