Quit looking! I didn't find the problem but I fixed it.

I did what I had to to get the Mail Merge to open, then I saved it as another template (maybe I could have just saved it, but the name was misspelled anyway).

Well, lo and behold, when I open the new template, it goes right to the Mail Merge screen, no SQL check, and no Windows Explorer data source window.
Works on both PCs.

Yay!