I have been setting up my Project Server 2013 multi-server test farm for a demonstration next week which will show my customer how you can configure web apps and PWA instances to use different or the same content DBs. (Generally, I recommend using separate content DBs for each PWA instance.)
In the process, I was setting up Project Pro 2013 with accounts and could not connect to any of my spanking new PWA instances.
Any time I attempted to connect while logged in as the farm admin, I received a message saying "No permissions to read Project Web App Enterprise Global file. The Project Web App Enterprise Global could not be access. Contact your Administrator."
Here's a screenshot.
After some fumbling to confirm I did, in fact, have all the permissions I needed, and researching internally and searching online, I decided that since I was running SP1 and the Nov 2014 CU, updating to the Feb 2015 CU wouldn't buy me very much, so…
I reran the SharePoint Configuration wizard on all my Project Servers one at a time. That solved my problem.