If you can't load your website in the browser and instead are faced with this error 'ERR_CONNECTION_REFUSED' then run the following commands on your vagrant box (I came across this error in Chrome):
1. Get the PID of nginx master process e.g. 'root 3861 1 0 14:43 ? 00:00:00 nginx: master process /usr/sbin/nginx -c /etc/nginx/nginx.conf'
ps -ef |grep nginx
2. Kill the master process
kill -9 19506
3. Verify once again whether there is any nginx process running or port 80 is occupied. If you see any process is bind to port 80, Identify the PID and check if it can be killed.
ps -ef |grep nginx netstat -tulpn |grep 80
4. Make sure the filesystem is fine and you can read/write to /var file system. Then Start nginx.
service nginx start