Success (after a fashion!)
After several more efforts to defrag my C: drive (all of which proved a waste of time) I applied some lateral thinking -- and came up with the following pragmatic (if somewhat inelegant) solution. Which I report here should anyone else have a similar problem.
Remember firstly that this is a production system - by which I mean that: No system = No income. The ideal solution would be to simply re-install the operating system, but I still have work that needs to be completed this side of Christmas, and my experiences with installing (or re-installing) operating systems if that if you do it in a hurry, you usually create bigger and more time consuming problems.
However, something needed to be done as it was taking anything up to 30 seconds just to open a folder.
Therefore: Since all my working files are stored in "My Documents", and since this is where there is considerable ongoing change to files each and every day, decided to copy "My Documents" off to another disk, and then give defrag another chance. This was not a trivial task - copying 2.8Gb took slightly less than four hours (to the D: drive, a 10Gb drive which was the original C: drive on the system).
Then disabled Power Management/Screen Saver/Norton AV and turning everything else off (by running MSCONFIG and unchecking everything except Explorer in the Start Up Group).
Rebooted system in SAFE mode and cranked up defrag (with all fingers and toes crossed). It hesitated for a l-o-n-g time around the 10% mark (which is when it has previously decided hat it didn't have enough memory and flashed me the two-fingered DEFRAG009 message).
Ten hours later (!) the disk is defragged - and I now have to copy the contents of "My Documents" back to the C: drive (can't easily use the system until I have done that because most applications - including Eudora and Palm Desk Top use directories in "My Documents" and it's too much hassle to reset all the defaults).
I hope that this description of how I got around the problem may help someone else out at some time in the future.
And I think that the lesson for the learning here is defrag is a very necessary evil that needs to be run on a regular basis. My case may be a bit extreme in that I add large numbers of relatively small files on a very regular basis (student tests) but the deterioration of system response went from "acceptable" to totally "unacceptable" over only about three weeks.
As soon as I have finished off current marking of tests, I will be pulling down the system and re-installing the O/S (should I stick with 98SE or go for 2000?). Also arriving soon is an external 40Gb backup drive which plugs into a USB port and should give me an extra level of security (have had a rash of burglaries around here recently so that will give me some peace of mind). Thanks to everyone that has made suggestions - and I hope that my experiences may, in turn, help someone else out there.
Feline purring - somewhat!
P.S. Couldn't get to Pprune for a while (for reasons apparent from above) but will be following up some of the later suggestions - Thanks!