Then the hello world image should work. Can you tell more about the machine on which you try to use Docker? Do you try to run it on a physical machine, virtual machine or inside an other container?
As I thought. You want to run containers in a container. More precisely a Docker container in an LXC container. You need to properly configure your LXC container to allow nested containers. Is this LXC container under your control or controlled by a cloud provider?
I know there is a way to run docker containers in an unprivileged LXC container and I did it one time after a similar question in an other topic. I think I followed and maybe modifed this solution:
But If I need an isolated environment for Docker I usually run virtual machines which you can do with LXC 4 too.