We discovered the problem. Everything works the way it should, but the course administration block (which has the "enroll me in this course" link for students lost its permissions except for teachers. I went in and changed the permissions to allow students to view the block and it still didn't fix the issue. Then, I changed the permissions for Authenticated User and that did the trick. Now all students and teachers that logged in with their account can enroll themselves in courses with self enroll enabled, but guests don't see the block and can't enroll themselves, only see the course.