One Solution:
I resolved the problem to the extent that the messages changed to:
"OK! Version: can't detect version on Windows"

The way I solved it was to install a completely separate version of Menalto Gallery. I followed their complete setup instructions based on my OS (Windows XP). Then I reinstalled and reconfigured XoopsGallery accordingly.

I did not change any permissions or do anything to cmd.exe.

Now, that I have upgraded XoopsGallery to 1.3.3.5. When I run the admin/check file permissions, the result is:
"File Permissions Appear to be OK."