Well this past weekend I took apart the iBook G3 to see if I could find the faulty connection. I was able to find a better guide for disassembly complete with a screw guide so you knew which pieces went where. Besides being way too complex for its own good the procedure went well. Although when we finally had the machine open gazing at all her inner glory. It became abundantly clear that I would need robot eyes and hands to find the problematic video card. I could not find a schematic for the logic board on line anywhere either, so I couldn't reason my way to seeing exactly where the video card was on the machine. (Of course in my search for a link to a program that repairs the logic board if you remove it and send it in, I found the following link which points directly at the faulty chip and where it is on the board).
In the end we put a shim in the machine and it now works about 33% of the time. Not acceptable at all. Luckily my boss gave me his old G4 as a bonus this year, so I won't be with out a machine.