I tend to agree with the logic board(s) conclusion, however one thing puzzles me. When I cloned the "good" OSX (onto a new HD), I could not use the cloned copy in either machine, although the clone appeared to work A-OK, and was identified in the cloning process as bootable. However, the original "good" OSX works in both machines...it just freezes in the problem machine. That makes me wonder if there may be some weird Apple kernel related issues with trying to run the "good" OSX in a machine it was not originally installed on.
I'm thinking I might put the original logic board back in, and try to locate a copy of 10.4 install disks. Not giving up yet!