Noting that the MDDs have terribly unreliable power supplies (that can get progressively worse over time with erratic voltages), it could be a possibility that the ADC display, drawing all its power from the MDD, makes it fall over when plugged in. The other thing is the graphics card - which model is it? Can you try another ADC graphics card? Remember that the Apple AGP graphics cards have special connector providing +28V for ADC power, which a standard VGA display does not use - this is the difference.

I'd try disconnecting things like your HDs, optical drive, remove any additional PCI cards, external peripherals etc. to lower the load on the power supply - then plug your ADC display in. Also try blasting any dust out of the AGP slot, and clean the connectors on your graphics card (you can use an eraser).

Interestingly, I found this link while researching ADC which details modding the display for standard DVI signal + use an external 24V power brick:

http://forums.bit-tech.net/showthread.php?t=188336

JB