It seems I made the mistake of Installing CS2, making a Ghost Image, deciding that was daft, uninstalling CS2, remaking the Ghost Image, using it and trying to install CS2 on one NESFA Computer and just InDesign on another NESFA Computer.
I eventually got the InDesign only machine to run cleanly after about 4 calls to Adobe over 2 different days, reinstalling the product 3-5 times (trying different license keys, deleting license files, and finally running CS3Clean with a smattering of System Restore in between to get back to known "good" points). Note that I had to run a CS3 tool to get a part of CS2 to install.
On the other machine, I've pretty much given up and am going to go back to the Ghost Image next time I feel like hitting my head against the wall, er, am awake enough and have some time to kill (which fortunately only means I need to reinstall the more recent Microsoft Patches and update the Virus Scanner), run CS3Clean first, and then try to reinstall CS2. By running CS2 before CS3Clean, I apparently got into an installation loop and there are parts of CS2 I can't uninstall or launch successfully (not from the ControlPanel, not from the Adobe Installer, and not by hand). And unfortunately on this machine I never got a clean System Restore point.
Let's see that was about 6 hours (7 PM to 1 AM ) Tuesday night and about 4 hours (6:30 PM to 10:30 PM) tonight.
And yes, NESFA has 2 (or 3) complete CS2 licenses and about 4 (or 5) separate InDesign licenses. So, this was all above board.