I have finally got it sorted out by disconnecting the hard drive and all significant USB devices (two external drives and a printer) and forcing it to boot up on my rescue disk. I then reverted to an earlier backup, and it is now working.
I will do what gregrocker suggests above, but what seems to be happening is that the system auto-detects USB Mass Storage devices during system boot-up, and waits (and hangs?) while autodetecting my Lexmark printer, though why it should think that that is a mass storage device I do not know. Is there any way that I can stop it doing that, for the printer and, possibly, for the two genuine USB storage devices?
The lesson I have taken from this is to change the order of my boot process - it was HDD then CD, it is now CD then HDD. This will allow me to stop it booting from the HDD by putting in a CD, if I need to