Wait, you're saying you have *two* IIcx's doing this crap? Seeing as how you did everything else, it does seem to be a component level problem, but on two different machines? Hmmmm.....

I've run OS 7.5.x on a IIcx without problem, and I see that you've also tried 7.1, which I know runs fine too, but perhaps create a System 6 boot disk, unplug the hard drive, and see what happens?