On restarting the Windows VirtualBox VM this morning, I initially got warnings that previously-mounted drives were not connected; this was true (Drive2, where the VDI hard drive file is located, wasn't yet mounted, and there was no CD in the CD drive). I mounted Drive2 and tried to start the VM again, but it crashed and restarted Linux; then it told me the VM was unusable, and I would have to revert to an earlier snapshot. This I did, only to discover it had rolled right back to before the Delphi 2009 install. I had to start again with Delphi 2009, further impeded by the fact that my CD drive seemed unable to read the Delphi CD (Greg made me an ISO, which worked fine).

Digging into the Help file, I found this:

When, on VM startup, a CD, DVD or floppy device is unavailable, VirtualBox by default prints an error message and refuses to start the virtual machine. In some situations this behavior is not desirable.
The behavior can be changed for the CD/DVD drive with the following configuration change command:
VBoxManage setextradata "YourVM"
   "VBoxInternal/Devices/piix3ide/0/LUN#2/Config/AttachFailError" 0
The equivalent command for the floppy drive is:
VBoxManage setextradata "YourVM"
   "VBoxInternal/Devices/i82078/0/LUN#0/Config/AttachFailError" 0
You will still get a warning message that a device is not available. Some guest operating systems may show strange behavior when using saved state or snapshots, especially if a previously mounted medium is no longer available when the virtual machine is resumed. 

This would seem to be at the heart of it. I had previously suspended the VM rather than closing it down; I'll avoid that in future. I've also run the two commands above to make sure a missing drive is not an issue, and I'm going to take several snapshots in quick succession to make sure if I have to roll back, I don't end up rolling back too far (although it was VBox that rolled me back too far; I only requested to go back one snapshot). I've also backed up the whole VM after the Delphi 2009 install.

This has cost me a day, and it's a bit worrying. If it happens again, we may have to conclude the VBox isn't ready for prime-time, and look at other options.