Ok, I promised Nige I'd update all this when it finally got resolved. Here goes ...
As you can tell, it's been a long time since I posted this. Well, I first needed someone with the CAT software to diagnose the problem. Thanks to Nige and his friends in this forum, I found an ex CAT mechanic that was now working on his own about an hour and a half from here. He agreed to come ... in 4 months! We're rural and that's just how busy these guys are. Anyhow, about 5 months later, he arrived, got the machine running in a matter of minutes and declared, "It's the display." I was thrilled it was the display and NOT the ECMs, but because I didn't just gamble and swap out the display when I first suspected it back last fall, I was without the machine several months, paid a mechanic to "officially" diagnose it, AND had the price of the display increase in the downtime by $200.00. I'm not grumbling; that's just the facts of the matter.
But that's not all ...
After a couple of weeks of using it without a hitch, once again, it wouldn't start and the screen was doing funny things. I was dumb-founded; the mechanic on the phone was dumb-founded; then I discovered that although the battery was drained, the battery and the alternator both tested good. Hmm ... "Could a vampire drain that I first suspected back 8 months ago in the stereo system have killed my first display and could it somehow be in the process now of killing my second?" (Earlier, I'd removed the removable security face of the stereo system because it wouldn't otherwise turn off. When I did, I'd thought I'd solved the vampire drain problem.)
Anyhow, the thought of the stereo still somehow draining the battery led me to take out the stereo system altogether (I didn't listen to it anyway.) With the stereo out, I then charged the battery, used the machine a little bit, and went on vacation. Weeks later ... weeks of sitting without being started ... VROOOM ... my CAT started right up. At last, I thought, "It's fixed and I can finally report back to Nige." Here's hoping I'm right. ALL the months, ALL the aggrevation ... all apparently over a silly short of some type in the sound system! Go figure.
All that said, thank you. Thank you, Nige, and everyone else for your help!