My iMac M3 won't wake up

On Friday my new iMac M3 arrived. I used the better part of the evening to copy everything from my late 2012 iMac to the new iMac. After that and after a while, it went into standby. Trying to wake it up, didn't work. It doesn't respond to the keyboard (not even Touch-ID), moving the mouse (didn't expect it, but if nothing else helps...) or pressing the button on the back (for a short or long time). So I unplugged the power cord from the power outlet.

This morning, it powered up fine. After a while, it again went into standby. And again it doesn't respond to anything. I unplugged it from mains power again.

Funny thing is, the small light on the shift key doesn't light up if I press that key. The keyboard is switched on. And it doesn't matter if the keyboard is attached via wire of wireless. The light simply will not go on.

But if I connect the keyboard to the old iMac via wire, the light WILL go on when I press the shift key.

I guess some settings (copied from the old iMac) are counteracting each other, resulting in me not being able to get my new iMac out of standby. But which ones?

Sincerely

Mathy