I didn't relate why because I didn't think anyone would be interested!
LOL
So, here's the details, although I can't relate the truly specific
details as I simply don't remember them.
While MS tech support, an engineer a couple steps above the normal
person you work with, kept looking at things, I simply sat here on the
phone with him, and observed what was happening. I found it interesting
that they used Teamviewer rather than MS's own supplied Remote Desktop
application. I wonder if that should tell us something. LOL
While I watched the tech, and at the end of each session, I did my
normal overall system shutdown procedures (I've more than one computer
here, often all are online), I realized one time that if the modem was
off, the computer would shut down. If the modem was on, it would reboot.
I figured there was some kind of software bug, but I had no clue where.
So, I let tech support do their thing until they eventually gave up,
called it quits, and filed it as an unresolved issue.
I've no technical education in this area, I listen to the experts, the
people who know more than I do, but I always take things with a grain of
salt. I observe what's going on, think and analyze for myself. I think
outside the box, asking myself "What if" questions even when the
question isn't logical. After confirming the fact that if the modem was
off, it worked, modem on it didn't, I wondered... What would happen if
I change the Ethernet card.
Yes, it was in a PCI slot, no onboard Ethernet.
The card was a relatively new Linksys card, it was still on their
website. I have a box of old cards, so picked one out of the box and
swapped. Bingo! Modem on, the computer shut down.
I contacted Linksys to see if there was any kind of firmware update, but
there wasn't , so I just left the old card in the computer, and never
looked back. It's just a suspicion, but I suspect some type of conflict
between the security update, Linksys software, and/or BIOS that was the
source of the problem.
It was an old Gateway that was on the market when XP first came out. I
was redoing everything to donate it to a local social agency for
someone's use. The original COA sticker was till on the computer.

The only copy of XP that I had that would successfully install was XP
SP1. Not 1a, 1. Then I had to go through the process of running MS
Updates manually. I don't turn on automatic updates at this point. As
soon as a particular high-priority update would install, the shut down
would fail. But there is a note in that particular update that if the
user had problems, free technical support was available. And I made use
of it. <grin>
AFAIK, the computer is still running. I actually had enough pieces
around here that it was a complete system including printer.