Thanks, helpifIcan.
I was waiting for someone (who said they might have one lying around) to lend me a sound card.
In the meantime, I wasn't even bothering to switch my speakers on anymore. I'd virtually given up hope and assumed it was a motherboard problem, as you suggested.
Then, today, I decided to pull one final desperate trick. I pulled out the cable from my USB hub (to which the usual 2 or 3 USB devices on my desk are usually attached) from the back of my computer and plugged it into a different USB port. Windows showed it was installing the device driver. I then turned on the sound, and .... it was back!
Unfortunately, because I've had the speakers switched off for the last couple of days, I really don't know if what I did...