Thank you for that suggestion. I did end up contacting Customer Care and had a helpful chat. Helpful up to a point, however. I was told to download the trial version, as my serial number is still valid, but the downloader assistant (or whatever it's called) has a bug and can't actually download Elements.
I've notified Adobe and am awaiting their response.
I've tried going back to the original download section www.adobe.com/go/getserial, but that page reckons my serial number is invalid.
The joys of modern technology!