If you or your trainee can't see any modules this is almost always because either the trainee (or you) are not assigned to a group, or you've made a group and unassigned all the modules. It can happen when you delete a group that has trainees assigned to it and they are not assigned to any other group.
Look for the Groups column to be blank when you look at any Enrolled trainees page (i.e. Manage > Trainees and courses, Options > Enrolled trainees)
Assigning the trainee to a group
Click on Manage > Trainees and Courses then Options > Enrolled Trainees. This lists all your trainees. Find the trainee in question and click Edit. Choose a group and save it.
Re-enabling modules in a group.
Check out this article on assigning modules. You need to be the account holder.
Trainee can't see a course, despite doing it before
This is almost always because the trainee has two separate logins - one might be an email, one is a username, e.g. firstname.lastname. Or they might have logged in using Facebook rather than their email or username.