I have an AWS instance that I shutdown the following way:
Unfortunately starting them all up again the reverse way, it failed at Zepplin with an error saying it couldn't create /var/run/zepplin due to bad permissions. I manually followed the symlink to /run directory and changed perms to 777 so other services could create directories under it. Then everything started fine. I suspect this is a bug in the Zepplin service start function?
@Rupert Bailey check the permission on the following directories
ls -l /var/run/zeppelin/*.pid
ls -ld /var/run/zeppelin
The permissions on these directories and files should be zeppelin:zeppelin, if not then change permission and restart zepplin and see if it helps.