Enrolment plugins enrol_cohort, enrol_database, enrol_manual, enrol_mnet, enrol_paypal and enrol_self have a "Default role assignment" setting (e.g. enrol_self | roleid) with the default value "Student". The ID for this is read from mdl_role. However, the student role can be deleted (from Site administration → Users → Define roles) in which case PHP Notice-level messages are generated by the code, e.g. "PHP Notice: Trying to get property of non-object in …/enrol/cohort/settings.php on line 39".

This appears to be the issue causing Trying to get property 'id' of non-object.