I also am having this issue after upgrading from 1.0.3 to 1.1.30 Getting:
Access to the path '--\App_Data\Dependencies\dependencies.xml' is denied.
From another installation, I can see that this particular file (and others in the dependencies directory) have the AppPool Process ID associated with it but the permissions are marked as "special permissions".
I also seem to remember having to give special permissions during the install process using the wizard on my initial setup (not during the upgrade).
I am using this link for instructions to upgrade: http://orchardproject.net/docs/Upgrading-a-site-to-a-new-version-of-Orchard.ashx