After adding libxcb.tcz to OnBoot, I got the graphical interface - the same as in Linux Mint, and I can set it up the same.
However, I previously explored the files and directories where the settings are saved (in /etc), and these are not being created in Tinycore. So the graphical interface appears to work correctly, but the settings are not saved (unless they are in a different place). There seems to be something fundamental missing.
It would be good to get this working, so we can have an easy method for users to connect to mobile broadband.
I think, in the future, more people will use mobile broadband than other types of internet connections.