This afternoon I finally got around to letting Software Update install the OS X Security Update 2009-001 for Tiger on my MacBook.
Being an idiot, I didn’t do a backup first. When the system restarted, it got to the grey screen with the Apple logo and the spinning gear, where it remained… for over half an hour.
At this point I gave up and switched over to my PowerMac, where an intensive Google session commenced. There appear to be a number of people encountering this or similar problems, but various suggested solutions didn’t work.
I was able to mount the MacBook on the PowerMac in target disk mode (which somebody on this Apple Support Discussions thread wrongly claims is impossible) and followed some of the steps listed at MacFixIt’s “Startup fails (particularly after a system or security update); solving” tutorial, specifically, deleting assorted cached OS files.
However, the MacBook still wouldn’t start, not even in Safe Mode.
So I then downloaded the standalone installer for the update from Apple. Despite being an Intel update, this ran on the PowerMac, and detected that the FireWire drive was a bootable Intel OS X installation. It installed successfully, and having ejected the MacBook drive, I restarted, holding down the Shift key to reboot in Safe Mode.
Bingo! The MacBook booted up. I restarted again, and it booted normally.
Panic over, and time to do a backup.
Hopefully this solution will prove helpful to anybody in the same situation.