GOT IT! Too weird, but I'll recount it here, in case it helps someone else
browsing.
As it turns out, it was my Norton Firewall. So yes, the two machines are
built to communicate. But what's weird is that disabling the firewall alone
wasn't enough. I had to configure the desktop machine (again, this is
specific to Norton) as a "trusted IP" And then again, simply listing the
machine as "trusted" without turning off the firewall, ALSO wasn't enough. I
had to first list it as "trusted", and then turn off the firewall. And boom
-- the files were all there. And what's further weird, is that, then I turned
the firewall back on, and it all still worked. So somehow perhaps, it needed
to get past firewall to have found the trusted IP configuration; and then,
once it was on again, all was configured OK. Further weird yet is that this
"trusted IP" thing is something that I never had to mess with when the
machine was working the first time. Who knows? I guess Vista just had to
browse around for awhile. --But those things were the key.
Now, for those who may be like me -- the "just gotta know" type person. Just
for the knowledge of what ultimately caused this, I went back in and removed
that trusted IP configuration. And boom -- no files. So, OK, that's in, I'm
thinking. So I put it back in, and again NO files. Yikes! And I had it
working, I'm thinking. Did I REALLY have to mess with this, just for the sake
of knowing. (Yes, is that answer.)
Anyway, after getting all in a knot for awhile, that's when I turned off --
and then later successfully turned back on -- the firewall. And it worked.
I'll post this in a fresh post so that it may help someone; but the nutshell
steps to configure the Norton Firewall are:
1. Open Norton Protection Center
2. Click on the second tab, "Norton Internet Security"
3. If it's not already, open the "Settings" section by clicking the "open"
4. Scroll down about halfway to the Web Browsing section, and then look for
the Personal Firewall section. Chances are, if the firewall is on, you click
the "On" link (It'll say Off, if you've disabled it), and then..
5. Click on the Configure button.
Almost there..
6. Under the Personal Firewall section, third link down says Trust Control.
Click here.
7. Middle tab says Trusted. Click there.
8. Click on the button that says Add, and then type in the IP of the machine
that you want to network with. (In my case 192.168.0.4) and then OK. If you
don't know the IP of what you're looking for, then do Control Panel/Network
and Sharing Center and click "View full map" to see your setup. Mouseover the
computer you're looking for, and it will show you its IP. (Now, if your
machine doesn't show up in this map, that's a whole different situation than
I'm talking about, and I'm not a network guy. So you'll have to figure that
part yourself.)
9. Once you've entered in the IP -- and this is the part I don't understand
-- that's when I turned off the firewall, and it worked. And then turned back
on the firewall, and it STILL (thankfully) worked.
So, if that alone isn't the end of the saga, as I'm typing this, working
through all the stuff to click, turned off the firewall and back on again,
and it didn't work. Oh joy. Fortunately, I had mapped the other machine's
drive to my computer, which now lists it as a "Y" drive on mine, right in my
windows explorer. And I was still able to access. So, at least I'm functional.
Now, by "not work" what I mean is that, in Network and Sharing Center, when
I clicked on View full map, it showed the computer, but I couldn't click on
it to see the files. Again, fortunately the previous map was still working,
so I was content. But all to not-understandable to me.
So, as I had nothing to lose (hopefully,) I clicked off and on the firewall
again (all the windows were still open

and everything worked again.
I won't be changing it again.
I hope this helps someone.