It should run fine sans LCD. Just hook it up. You could get an inexpensive LCD monitor and build your own imac. Is the problem the logic board flaw that those are notorious for? It doesn't sound like it as if it were it wouldn't output any video at all. It may just be the cable running from the board to the screen. Not a hard fix.
Yea, I believe it is the logic board, as that is what they told me the 1st time. The screen goes dark... as if the backlight is gone. Pressing firmly on the left front corner can sometimes...briefly...bring the LCD back. It does output to the external w/o any problems. It works fine in that area.
An iMacBook would be interesting. At this point don't really have any solid ideas.
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