Hi Phil
You should be able to access via SSH with root user or other user if you have create other user than root.
The procedures are described in below links, you can double check if you have missed any steps.
VMware KB: Using Tech Support Mode in ESXi 4.1 and ESXi 5.x
http://www.vmwarearena.com/2013/07/enable-ssh-and-esxi-shell-for-esxi-51.html