I tried doing the usual things: Reset the PRAM, reset the PSU, try to boot from OS X install disk. Seems the machine doesn't even know the CD drive exists, because holding down C on startup doesn't boot it. Holding down the space bar doesn't try to eject the disk (so now I have two problems). Holding down Option brings up the Startup Manager boot menu, but there are no boot options (neither CD nor hard drive, just the reload and go arrows). With that, I'm suspecting a controller failure rather than specifically a drive failure.
I don't have any other machine that takes SATA, so I may buy a SATA-USB external enclosure to confirm that it isn't the drive. I haven't tried Target Disk mode because I don't think the drive hardware thinks the drive exists, plus I don't seem to have a FireWire cable anyway.
Tomorrow I'll pick up a 4" Mac Mini disassembly tool (putty knife) at the hardware store and see whether it's anything obvious like a loose connector. Failing that, there's an Apple authorised repair shop nearby that might be able to fix it for an exorbitant fee. Or, I could just bite the bullet and get Amy a shiny new MacBook (with educational discount!) so she doesn't have to sit in the cold office to do research for school this winter.