I had the same problem with a 933 Mhz ibook - i.e. screen freezing after a few minutes, sometimes not booting up and screen remaining blank. Took me a while to figure it out, as it appeared to be heat related - I could put an external fan on it and it would stay working for a lot longer. Thought it might be the internal fan not working, but I tested that (connected it to a battery) and that was working. The fault lies in the Graphics chip which sits under the larger second part of the heat sink. What happens is as the chip heats up, it starts to come away from the logic board (cracked solder perhaps?) and stops working. Not helped by the fact the logic board is very flexible at this point. The solution is to put a shim between the graphics chip and heatsink to keep the chip pressed hard on the board.(conveniently in this model the heatsink for the CPU is separate and does not require a shim) In the absence of any copper sheet, I found the ideal shim to be a 5 old half penny pieces (that is UK pennies as...

I have a first version 1.8 20inch imac, which had black screen and wouldn't work an external monitor iether. everything else appeared to work and I could read the hard drive when hooked up to my powerbook in Target mode. Checked the capicitors and nothing obvious blown. Checking closely one of the capicitors near the screen output cable (there are 2 sitting together on the logic board here) had a very slight bulge in it. I changed it and voila! screen back and a happy mac user again! Cheers Jeff PS - cost of capicitor £0.40 and just my time and plenty of guidance on ifixit!