Hi Fiona,
A wiser head here may correct me, but my understanding is the only courses that show in the My Courses block or heading in the Navigation block are those that a user is directly enrolled in (course based enrolment vs category based enrolment).
That said, your custom user "should" be allowed to see the Courses link in the Navigation block, that will show a list of all categories on the site - they can then enter courses through this path. Check that in Site Administration -> Appearance -> Navigation, the Navigation block is allowed to display category headings, as this will help your users locate what is of interest to them.
Hope this helps!
Lindy