Basically the user was complaining that they could not turn layers on and off in the Table of Contents (the left hand pane) but they could go in to the properties of the layer and turn things on and off from there, but this was very frustrating and tedious. They had tried multiple MXD files, both their own and those created by other users and still no joy, and other people had opened their MXDs and they were fine.
What the problem actually came down, after some serious google-ling, to was the fact that the user was using two monitors and had them set-up with the right monitor as the primary and the left as the secondary. Once I got them to switch them around, i.e. the left monitor as the primary display, everything worked fine.
An odd a very obscure issue, which I thought I share in case anybody every encounters it again.