Hi,
We have a brand new SharePoint 2013 installation. We have 2 web applications, onw for our MySite host and one for the actual intranet. We noticed we had problems with our tasks and figured out we needed to install a Work Management Service. When doing so, we got locked out completely from our intranet site which is based on a Publishing Site.
No matter what rights we have on the site (site collection admin, site owner, etc), SharePoint tells us we do not have access.
We are sure the issue is with service as we restored all of our databases and everything came back to normal until we reinstalled the Work Management Service.