Thank y'all for alllllll your hints and suggestions. I went back to the EQ Forums and read everything I could find about EQ5 and any issue.
Turns out that Microsoft Windows Update KB943460 was the problem. Electric Quilt could no longer read folder names or filenames with spaces. All the information about it was in the EQ-Forums but not all in one location.
I had deleted the update but it seemed to have no effect. If I had been sitting here watching every thing on my screen, I would have noticed that the update was automatically installed again when I rebooted the computer.
So I changed my Automatic Updates to "notify me but don't automatically download or install." Sure enough, I rebooted and the auto-update icon appeared. This time there was a window where I could make a choice. I chose to never be reminded about that particular update again!
I'm a Happy Double-Clicker again!