Hi there. Thanks for the hints and the cool picture

!
I rebuilt by old rig (old MB, CPU and stuff) with the Cougar and it instantly works flawless. So the PSU seems to work here (and has since 2 years).
On the new rig I stuffed all cables into the right sockets (verified multiple times, they are also protected from wrong assembly by coded connectors) and I tested all combinations of 20/24-pin ATX and 4/8-pin CPU to no avail.
The new rig with an old ATX PSU worked instantly (!).
This leaves me with:
old PSU + old MB = works
new PSU + old MB = works
old PSU + new MB = works
new PSU + new MB = no power-up
I haven't tried hardwiring pin 16 to GND. I know it's about the same as pressing the power-button (not exactly) but I feel coward fumbling with a bent wire here ^-^ .
Also I think it *will* power up because the Cougar-PSU *does* work - but in the old rig.
I read some PSUs won't power up if there's no load on both 5V and 12V wires so I connected the Gfx and drives to the PSU, but it didn't change anything.