Thanks. I deleted everything and started over going through those steps. I've got WP installed, the correct theme active, all the plugins are there, etc. So that's good.
But it still won't connect to the database with all the existing posts, etc. in it. Connects fine to the new db I created for installation but when I either try changing to the full db or copying tables across, it gives me a 500.
So, what does that mean? Could the db that won't connect be a different and incompatible version, if such a thing exists? I've moved WordPress sites between servers before and never had this trouble and I'm at a bit of a loss.