Thanks everyone for your suggestions. The answer has turned out to be very much simpler. I realised that the file "bzImage" (note the upper case I) referred to in the instructions at
http://www.tinycorelinux.com/install.htmlin paragraphs 5 and 6, was misread by me as "bzimage" (lower case i).
So grub was looking for "bzimage", and couldn't find it because it was actually called "bzImage". I have accessed Tiny Core's "menu.lst" file from my Mint linux installation and simply corrected the line "kernel /boot/bzimage quiet" to "kernel /boot/bzImage quiet".
Alternatively, no doubt I could have gone through the installation process again, and done it correctly (bzImage - upper case I).
In an effort to excuse myself, perhaps I could comment that I find this a problem with some "sans serif" fonts. i looks too much like I, and they both look like l (lower case L) especially if the rendering is small on the screen or when printed. In my opinion, for what worth, I think it might be better if computer instruction were prepared using a "serif" font.
Anyway, it works ok now. Hope that will be helpful to someone, several someones, perhaps!