First, thanks to all who replied and jonh, your question about the
console going to the serial port proved quite prescient. Keeping copies
of my grub.conf file at various stages of the process reveals that at
the point of death grub.conf started:

serial --unit=0 --speed=9600
terminal --timeout=10 serial console
# grub.conf generated by anaconda
#
# Note that you do not have to rerun grub after making changes to this
file
# NOTICE:  You have a /boot partition.  This means that
#          all kernel and initrd paths are relative to /boot/, eg.
#          root (hd0,0)
#          kernel /vmlinuz-version ro root=/dev/hda2 console=tty0
console=ttyS0,9600 
#          initrd /initrd-version.img
#boot=/dev/hda
default=1
timeout=5
splashimage=(hd0,0)/grub/splash.xpm.gz
hiddenmenu
title Scientific Linux SL (2.6.9-34.ELsmp)
        root (hd0,0)
        kernel /vmlinuz-2.6.9-34.ELsmp ro root=LABEL=/1 acpi=off rhgb
quiet console=tty0 console=ttyS0,9600 
        initrd /initrd-2.6.9-34.ELsmp.img


Investigating further, I found that I had put SL_enable_serialconsole
into my standard list of RPMS.

Thanks again for all the help and do I assume that
SL_enable_serialconsole is normally a safe thing to have installed?
Presumably it's just a quirk of this machine or is this common?

John