Hey thanks for the kick in the behind. MimeTypes.... I would have never figured it was that. It certainly opened my eyes to it. Looks like I got some more reading to do on its importance. I did exactly what SmallDog suggested, and it worked. I was seriously going nuts trying to figure it out. It never crossed my mind that maybe it was the server.
And thanks for the link DanceInstructor. That really helped clear things up. I have put in a ticket to my provider to update the mime-types on this dev server to match my other server. I added the css htaccess line from the Mozilla link. That got the page to display the css right.
I don't know if it was the way I was googling, but when i was trying to figure this out initially, my searches for "Firefox not displaying css with strict doctype" returned nothing about mime-types, or the possibility of it being the server.
Thanks again guys.