I'm adding this now, not because it helps clarify things, rather because - in my mind at least - it makes it all even harder to figure out what's up short of there being more than one fault on more than one machine.
I booted up a test machine on which I have KDE4 installed. With K3b, once again I burned the same data. This disc runs fine on itself, but is not seen by the Dell Inspiron running xFce. 'Ha!' I thought, 'there's something up with the xFce install.' So, in order to hopefully confirm that, I put the KDE burned disc in the first machine - I'm sure I've lost anybody reading this by now - which produced the first three suspect burns yesterday - and just to confuse me even further, it read it, no problem.
I'm now giving this up for the time being. I'm going to hope that if I burn all the CD's I need on the KDE machine, they are going to be generally readable by others. I can see no real pattern in this, apart from maybe there's something cockeyed about my xFce installs and maybe the LXDE one as well. If anybody can help me find some sense in it I'd be delighted. The only other thing I can think is that there is some disc/device configuration thing I should check -but that's beyond my skills at the moment. And if I get the time and energy over this weekend I'll download the xFce ISO once again, do a new burn of it, and do another install.