Attach 15-inch Macbook pro screen (with broken logic board) to 21-inch iMac (with broken screen)? I am curious to know if I can take the screen from my Macbook Pro (15-inch, 2010) and somehow use it as a display for an iMac (21-inch, 2012) either through a direct connection to the logic board's display pins or via the mini display port.  The logic board is dead on the laptop and the screen is dead on the desktop, so between them, maybe I can have one functional computer.
No. The internal connectors are incompatible between the two; different size and different pin-outs. And there is no functional way to route the display signal through the mini Displayport from one to the other.