Sorry, finally got around to this again.
It is indeed the ZG5 model, booting TC as a livecd. I found that 3.x will boot properly with just the "tinycore norestore" (adding base not needed) command - have not tried 2.x since but I assume that would be the same.
However... as far as I'm aware it shouldn't be even trying to restore anything from anywhere. I've never used it as anything but a livecd and as far as I can tell, there are no TC related files being stored anywhere on my machine, or on usb sticks, sd cards etc. Same deal with the 1.x versions. Very puzzled. Any thought as to a solution anyone?
EDIT: Same behaviour even on a completely blanked machine running from CD. Well, I'm stuck then. Guess no more TC for me.