|The analog board connection cable.|
|The top and bottom large solder joints are suspect.|
I opened the computer up to investigate, but I didn't see anything obvious. I started it up while open (DANGER!) and noticed that slight pressure on the analog board connection cable would cause the video to come back temporarily.
I looked closer and noticed a questionable solder joint which seems to correspond to video out, according to this Macintosh Schematic (J7, pin 1, VIDOUT).
I'm not sure I will have time to fix it before January, but it looks like it might be an easy fix.