Blank screen and odd behavior of MacBook and iMac

Hi there,

when I connect my display, it is recognized by iMac (2012) and Macbook Air, it shows up as LED Cinema Display, speakers, mic, iSight camera, USB ports are working and I can move the mouse cursor where the display should be.

But the screen is black. No dim light, no faint image under a flash light, it is pure black. Additionally the iMac seems to have micro freezes or at least the mouse moves very slow and stutters when I connect the display. The MacBook Air's internal display shows artifacts and it also seems to freeze and the mouse doesn't react well. As soon as I unplug the display, everything goes back to normal.

Can only the LCD be the faulty part here? How can I find out what needs to be replaced? I've read about voltage checks on power supply and logic board and test points, but where do I find a 'map' of these boards to identify these test points?

lg, Alexander