Thanks to Mirek Sopek, the folks at Mako Lab diagnosed why my new WordPress blog template was going all wonky in Internet Explorer 9. Even after I’d discovered that the problem was that I was declaring the HTML page with Quirks, I’d put the type declaration in the wrong spot. I put it at the top of header.php, thinking that would put it at the top of the HTML page that WordPress assembles out of various files. Nope. You have to put it at the top of the index.php file. D’oh!
We still don’t know why it worked on my copy of IE 9, at the same version level and both 64-bit.
Thank you Mirek and Mako Lab! I would never have figured this out without you.