For what it's worth (you probably got this running by now) this my first foray into Nginx and the setup was far from trivial.
First off I had no idea where to set this up (/var/www?) and under what user (local user? www-data?) but eventually just made it up. Looking at various Nginx-with-PHP tutorials, it appears to just do what you want and hope for the best. I'm not bitter.
Anyway, I ended up deciding to go with a subdir of /var/www so I could potentially have other sites in there if I wish, and I chowned everything to www-data (and when running the console/composer tasks I `sudo -u www-data`) and this is the config I ended up with (and it worked!):
try_files $uri /index.php;
fastcgi_pass unix:/var/run/php5-fpm.sock;
It's pretty much what you have so I'm surprised yours didn't work - maybe it's the "/" prepended to "index.php" in the try_files rule.
Good luck!