There has been some pretty complicated issues with this server, once again. My current hypothesis is that the combination of badly configured backup processes and the buggy CUPS server together filled up the root disk, leading to a situation where MySQL database was not able to start any more. And that led e.g. me being unable to log into Ubuntu regularly via Gnome desktop. Also, it appears that either caused by this mess, or regardless of it, my main data disk (external USB Lacie) had got its “superblock” corrupted — and I did not find a way to fix it so far.
Well, luckily it was possible to log in via console, and (with some help) I have now deleted enough stuff from the root so that this system runs again. I also took the opportunity and finally did some memory upgrades: firstly, the default memory chip (512 MB in this Proliant ML110 G3) was replaced by two 1 MB chips (regular Kingston DDR2 value chips). Secondly, I got a bigger disk (not USB this time) and plugged it into the second SATA slot inside the Proliant. Seems to run ok: it is Samsung Spinpoint F1 750 GB model (more info here; a promo pic below). Now, if I only can find a way to access that corrupted Lacie USB disk somehow — it was formatted in FAT so using Windows software is an option here, too. And understanding what crashed the disk in the first place would peace my mind as well.
frans goes blog 
Another question in this equation is, just how much “more disk” one needs. When I had copied from the workstation all those Word, Excel, Powerpoint documents that I think I should keep, in addition to all image, video and music files, roughly 100 000 files had been transferred (~150 GB, I think). It would make no sense to keep all this data on hard disks, but mostly two things — the video files are nowadays utilizing better compression, and the arrival of affordable terabyte-class disks — has made it possible to continue copying everything in one’s personal archives. Keeping at least videos in DVDs might make better sense, of course, particularly as our camera is not a HD one, so DVD is good enough for them. But it is just the most simple backup mechanism to make a sync from one hard disk to another.
Corrupted superblock means something went wrong with the filesystem itself. It’s unlikely that this was caused by disk being filled up.
At least on ext2 filesystem – don’t know about FAT – there’s a spare copy of superblock somewhere. Try googling “corrupted superblock”, e.g. these hits:
http://lists.debian.org/debian-user/2001/04/msg03364.html
http://www.adminschoice.com/docs/fsck.htm
P.S. You might find stuff to delete under /var, e.g. /var/log. Command ‘du’ helps you to find big files.
Yes, at some point I was still able to to see the backup superblocks, and I hope they are still there. (Needed to get the other disk in and system running first.) Thanks for the tips!