Moving one site from one machine to another

I'm trying to move one site in a multi-site installation to a new machine, and I'm failing miserably. It's up and running and looks fabulous on machine A. On machine B, I installed the identical WordPress version. I copied the theme folder from machine A to machine B and site-wide enabled the theme on machine B.

I then created a new site on machine B with the identical name to machine A. On machine B, in the site of the identical name, I set the theme to the one I'd copied from machine A.

I then exported the database using Tools->Export from the site on machine A and imported it into the site on machine B.

The good news was the data showed up on machine B (although the importer kept reporting duplicate posts for a brand-new site). The big problem is that the look of the site on machine B is crap compared to the look on machine A. The menus are all set up wrong, all the theme's settings are set up wrong (or were never moved over), and so on.

If I want to move a site from one machine to another, and keep all the fiddly bits intact so I don't have to go through and completely rebuild the new machine, what's the best way to do it? I'd really appreciate a step-by-step so when I'm done, the site on machine B contains identical data to that of machine A and looks identical as well.