Thanks to Steve for alerting me to the 10yearsofscrobbling.com tool. That digs back through your Last.fm profile and reports back the first track it finds. Mine was Paradise by Uriah Heep. Since I have never owned any Heep, I suspect I must have started out by listening to one of their radio channels.
Prior to scrobbling, I used to track my listening with a manually maintained blog. You can still see it, including the final message that I was upping sticks and moving across to Last.fm to track my listening. I had a strong urge to be able to give a definite answer to questions like “what have you been listening to lately?” which was hard to pin down without records (no, not those black, shiny vinyl disks!).
I am still delighted by the way Last.fm supplies me with all sorts of statistics about what I have run past my ears in the seven years since; I wish I had started ten years ago when the audioscrobbling service first became available.