AWS Ubuntu using public/private key ssh, trying to start a deamon asks for password

Generally you need to perform Docker commands with sudo. Try this:

sudo service docker start

If you would like the default user account to perform Docker commands without sudo, then you'll need to add ubuntu to the docker group:

sudo usermod -a -G docker ubuntu

You can then test the permissions with something like:

docker info

If you get a permissions issue, you may need to disconnect from the EC2 instance, then reconnect.