Success. Kinda. I successfully installed the driver for my new M-Audio cable, and the system picked it up. Still no signal to/from MT-32 though. So I followed JHarris's instructions about identifying my MIDI device through Dosbox, and found that my MT-32 is noted as #1. Then I tried to alter the Dosbox conf file for the game via the DFend Reloaded (DFR) front end. It only provides a viewer for the conf file, and I couldn't find any way to change it in DFR. So I Dl'ed a simple text editor and went looking for the SQ3 conf file.
I looked in every single dir in DFR and Dosbox, and what I found was a dir within DFR called CONFS. Upon getting into it, I was SURE that was going to be it, as it had conf files for only 2 games; SQ# and Freddy Pharkas. (The only 2 games I have installed at this point) So...... in I go.
THIS SQ3 conf file is HUGE! It has to be at least twice as long as the one I had just viewed in Dosbox. It was also different in places. For example, the Dosbox conf file had the lines config= (as vs midiconfig= that had been in the viewer) and device=default (vs mididevice=default). That could be though, because they were listed under the [midi] heading in the config, so it was just ASSUMED that those lines were for midi. Probably so. At any rate, I typed in the #1, as JHarris had said. Then I went to the viewer, and it said midiconfig=1 midiconfig=1. sigh. (still no sound)
I went back into the DFR SQ3 profile, and clicked on the midi option. Under TYPE, the option "intelligent" was listed.
Under MIDI DEVICE, the option "default" was listed. Below those, ADDITIONAL SETTINGS, with an open line under it. Taking a shot, I entered the number "1" in that open line and saved. THAT did the trick, and the music dam burst. (I had to do the same with the Freddy Pharkas config, before IT would work.) Apparently, I'll have to do that for each of the games I will install on it.
Now don't get me wrong, I'm happy the thing finally is working, and I can go back to wasting my time in more productive ways.

BUT.... as these computers and their operating systems become more advanced, aren't they supposed to make things EASIER and QUICKER for heavens sake? I've set up 7 different machines with my MT-32 over the years, and although I've had hiccups before, I haven't had to go identify and alter conf files, AFTER determining what ID# my MT-32 had. For Pete's sake, I never even knew it HAD an ID #. (Thanks again JHarris!)
What did I learn?
1- No 2 midi cable are alike.
2- Never assume that when you plug any old midi cable into your brand new, 4 on the floor, space age, streamlined, do everything but the dishes machine, that it will simply recognize it and know what to do with it.
3- How to use Dosbox to ID my MT-32, and make the appropriate notation in the game settings within DFR.
Lastly, I'm still not convinced I was in "THE" SQ3 config file. It seems like I would have HAD to be, but if not there... where?
Mike