A guy at the Fnac store in Valence succeeded in erasing the memory of my machine. Funnily enough, that operation thrilled me, because I've been operating inexcusably, for ages now, in a totally stupid way. I've had a nice explicit list of all my confidential codes in a folder named CODES sitting in a remote corner of the memory of my computer. This was most convenient when I wanted to consult my bank account, or order a book from Amazon, say... but it was totally crazy from a security viewpoint. Yesterday, I finally rectified that stupidity... and that might well be a positive lesson from this mysterious crash.
When I took my iMac home, I set about reinstalling the system from scratch, using my original CDs. Unexpectedly (for me, in any case), the installer suddenly asked: "Would you happen to have a Time Machine backup, which could be used to reboot your Mac?" I said yes, with enthusiasm. And that's exactly what happened during the next ten or so hours. Slowly but surely, my iMac was restored, magically, to its pristine state! Thank you, Time Machine!
My advice to all Mac users: If you don't have Time Machine yet, think about acquiring it. Meanwhile, it was reassuring, too, to know that Carbon Copy Cloner had done its daily job, providing me with a perfect copy of everything in my iMac at the moment it crashed.
The two backup tools constitute a tandem, apparently with a bit of overkill… but it's better to be too safe than not safe enough.