If you have everything setup and your site root is not in the normal location (such as /home/user/Projects/site) and you see "File not found" in the browser, but "Permission Denied" in the nginx error log, you have a permission problem:
If selinux is enabled, you must either disable it or configure the folder using chcon
NGINX User needs "x" permissions in every parent directory. Make sure /home/USER has chmod a+x permissions.
Check every parent path with: namei -om /path/to/check
See https://stackoverflow.com/questions/6795350/nginx-403-forbidden-for-all-files for details.