OK. Following Juanito's advice, I started with a fresh installation of microcore, unpacked on hard drive and booted there (I guess "scattered" is what you call it) to which I (manually) added Xlibs and Xprogs (but not Xvesa), and later Xorg-7.5, Xorg-7.5-lib, Xorg-7.5-bin, Xorg-fonts and Xorg-7.5-xgi.
By the way, unpacked, microcore was a mere 9.5 MB. After adding the above, it has grown to over 50 MB. WOWOW! I guess that's a price the security paranoid must be prepared to pay
(and the reason why tinycore compromises with the much less desirable Xvesa - to remain small).
Now, with no special booting codes, the new system boots into a shell with user tc logged in. Entering 'startx' gets the following error message:
cat: can't open '/etc/sysconfig/Xserver': No such file or directory
So, I added a file named Xserver to /etc/sysconfig with "Xorg" written in it and rebooted the system.
At the end of the booting sequence the system now hangs for 10 seconds (it seems about to start the X server) but then gives the following message and boots, again, to a shell console:
hsetroot[3702]: segfault at 88 ip 08049cb4 sp bf927350 error 4 in hsetroot[8048000+4000]
tc@box:~$
Have I forgotten to add some required extension, or does anybody know what's going on here?