Here's a word to those of you who might be embarking on a similar task to mine, and might be similarly clueless as to the inner workings of the localhost (which kinda sounds like the breeding ground for some Alien-inspired, inhuman, possibly undead parasite, coming to catastrophic maturity up in the attic, just a few feet away from your slumbering head...)
If you inherit your Funding Body's old laptop, and migrate the contents of your old one to the new one, you will turn on said new one with a gasp of joy! There is every last bit and byte of your old life, miraculously and painlessly appearing on the screen of a faster, bigger, cleaner machine!
Then, when you discover that Mountain Lion requires you to reconfigure your Apache server and all your associated PHP-y, SQL-y things, you sigh in annoyance. But never fear - the same guy who wrote the foolproof explanation of how to set it all up in Lion has also written a Mountain-Lion-specific version.
And it works! Like a dream! Until you try to run your own stuff on localhost, and it tells you it can't connect to your database.
Now, run with me here: you have migrated the entire contents of your old machine to the new one, yes? You've got all your browser history, all your preferences, even a full trash can.
What you don't have is any of your databases. You need to recreate them before you can do anything.
Do not ask me how long I struggled with this before figuring it out... and do not ask how I figured it out, because actually it was the Funding Body who had the idea - which I initially poo-poohed, before giving it a try.
(You can read between the lines of this post to guess why I haven't yet written about my fantastic experience at the Performing Documents conference in Bristol last weekend...)