It was a file permission issue.
All files on my website were set to a permission level of ‘644.’ Once I changed the permission level to 705 (
chmod 705) everything worked. Note that I changed it to 705, but 755 will also work. I also changed the folder it was in to 701 (to hide it, but still be executable by the server).
Aside: I still don’t understand why my .PHP file worked on the other server when it was probably set to 644?? How could Apache execute the script without world permission?? Does Apache not need world permission?? Just a few questions I still have…