Umm... my deepest apologies to everyone. 
In one of my posts I said it's probably something really obvious that is right under my nose?
Well, Jac in http://www.gamesas.com/topic/1513057-relz-morrowind-overhaul-sounds-graphics-30-thread-6/?p=23881564 posted a link to fixing BEX errors, and I checked it out and made the adjustments, although I had set all Data Execution Prevention to off at some time in the past. I think that sometimes Windows Updates must reset things.
Well, I checked it again and Morrowind was not listed as an exception, so I reinstalled everything from scratch, added Morrowind.exe as an exception to DEP, and I could start a new game!
There were some errors and crashes, MGSO3 did not complete a couple of times and I had to start again, textures and meshes were reported as not being found and a few other glitches, but I started another character and did all the Seyda Neen quests as far as finding the killer and getting his house. And I could add the extra mods I wanted and they seem to work as well.
I was also able to load the saves with the other character I made on the weekend and also some saves of different characters I made over the years.
So, at the moment, it is running well and looks fantastic! 
I set Distant Land to 12 cells so everything looks great until the fog comes in, as I find that maintains the atmosphere of mystery. I still do not get why it worked sometimes and then stopped, or stopped working after re-running the installer to change settings, but it is working now.
And the MGE-XE shaders makes the water edges look SO much better than some of the lesser versions.
I don't know why Windows does this. And I have said before, my next card is going to be an NVidia!
The installation also seems to work better for me if I re-boot and run Registry Cleaner between each stage. One time there were 19 errors in the Registry after uninstalling Morrowind and deleting MGSO3 from the C:\Morrowind folder.
Anyway, as well as turning off UAC, ensuring there are no other installations of Morrowind on the system and checking the Registry, I would suggest that the Installation Instructions includes how to turn off DEP for Morrowind.exe:
Start -->Control Panel -->System and Security -->System -->Advanced System Settings -->under "Performance" section - click "Settings" -->Data Execution Preventionclick "Turn on DEP for all Programs and Services except those I select:"Click "Add" and Browse to Morrowind.exe and select it.
Of course, Windows error messages would be more useful if they told us WHY they stopped the program from working. 
My deepest thanks to everyone who pitched in to help!
Cheers!