I shall worry no more!
After a good bit of bollocing around, I found that it was in the devices list, but it was under the wrong heading (under system rather than DVD drives), and it had an error. It was that the driver couldn't start, which is why it wouldn't appear in My Computer.
After spending well over an hour trying to find a new driver, I find a neat little page telling me that Vista uses the same universal driver for all DVD drives. Woopdy-bloody-doo I thought, my Vista is broken
But, after another hour of googling (I have a very short attention span and tend to drift off into other things), I found that Vista has a known problem with a registry key that gives error 39, same as mine, with certain DVD drives, and can start any time. So I deleted the key as it said, rebooted, and weh-hey, DVD drive back again!
Now, it even plays the DVDs it couldn't before. No idea why that key is there, it seems to be another one of Vista's "fixes without a problem". Absolutely thrilled right now, never mind having to worry about the warez, but a whole week without internet? :eek: