I installed Neo4j on Ubuntu 12.04 using these instructions: http://www.neo4j.org/download/linux
wget -O - http://debian.neo4j.org/neotechnology.gpg.key | apt
You need to add the following entries into the /etc/security/limits.conf file
root soft nofile 40000
root hard nofile 40000
You need to start the service as root or using sudo
When you do that, the user that ends up starting the service is the root user.
If you dont have an entry in the file for the root user, then it would not work.
So, you just need to add those entries in the file and then reboot your server.
I had the same problem and that is how I was able to resolve it.