My external 1TB drive appeared to be empty!
so I rebooted
Booted my laptop, and find the external 1TB is not recocognised!
There is probably nothing I can't recover from elsewhere for
the extrenal drive, but how do I rescue the desktop system?
I'd really like to recover the external drive too!

attempting to mount the drive I get...

root@randir:/home/beckwith# mount /big
mount: wrong fs type, bad option, bad superblock on /dev/sdb1,
missing codepage or helper program, or other error
In some cases useful info is found in syslog - try
dmesg | tail or so

i like using GParted live CD and the "testdisk" commandline utility on it. BE CAREFUL, no guarantees concerning data-loss what-so-ever. There are tons of data recovery tools/CD's. you may want to do your own research first.

I tried various things, eventually booting the LIve Debian dvd, mounting a few
things then "install-grub". However - external drive - gpart could find no
partitions on it. So I have reformatted it. A mystery. I have lost 3 weeks
of backups that were on it, that were not burned to dvd.

testdisk can recover "lost partitions" semi-automatically. and if you know how to use fdisk "properly", that may have been a method also. that doesn't necessarily mean absolute recovery, but certainly had potential. sorry for your loss -- at least it was a backup and not solitary.