It turns out that my dead hard disk is still well under its five-year warranty, and that Seagate, the manufacturer, has an efficient online return system that helped me diagnose and then set up a return merchandise authorization (RMA) for it, including printing a shipping label for me.
So rather than go through the rigamarole of trying to rescue any data from the drive (as far as I can tell, it's not even spinning up), I mailed it off to Ontario a couple of days ago, and Seagate will send me a new replacement that I can drop in its place. In the meantime I'm using the stock MacBook hard disk, and it's working fine.
Because of my backup regimen, I lost so little data that all I've had to do is go through a few pages of my Flickr photos and re-import the missing ones into iPhoto—nothing else critical is missing. At least not that I've discovered so far.
So I should have a new drive to put into the MacBook next week, and I can use the one I have now once again as an external backup. One thing I do need to do is take some of my recent backups offsite, because right now I'm protected against failures, but if we get burglarized or the house burns down, important data could still be at risk.
You should do the same with your backups. You do have backups, don't you?