I added an AD user to group "Site Members" in a SharePoint 2013 application. Group "Site Members" has Contribute permissions at the site root, and there are no restrictive permissions listed when clicking "View Group Permissions" at the site root. This user cannot access the site root. I don't know where to look at this point - I don't see logs pertaining to site object access.
What else is available to troubleshoot, or where can I look for more detailed information?