Could an electronic KVM switch be of any use?
The computer keeps running, unless someone presses the power button (which is unavoidable
), the screen stays empty, even when the mouse/keyboard are activated (moved/pressed), until you switch to the correct 'port' (A/B would be enough, AFAICS), and with a little luck that can be protected by a key-operated switch (did no research on that).
Turning off all leds could be impossible without tinkering with the BIOS, unless you have connections with mainboard manufacturers
The sound of the harddrives & fans, probably depending on the load of the system, would still reveal it's not off, though...
And then someone pulls the power-plug from the back of the powersupply