Ok. Did as you suggested. It only took less than a minute, then called for
a "restart", which I allowed. When the computer came back up there was no
Norton to be seen. (Maybe it was uninstalled quickly because I had never
enabled it to begin with).

I got a balloon from Windows telling me I didn't have any anti-virus
programs installed.
The Windows firewall is on, but it said no virus protection software was
detected.

I figured "good", and then proceeded to try and install the AVG software.
The installation started, extracted all the files, etc., then a message came
up saying that it had detected another installed anti-virus program and
didn't recommend continuing unless I got rid of whatever it is. So, I
aborted the installation.

Windows Defender?

Eisboch