Hi Dan
I understand in this case you do not have any route to the appliance and it is not responding on ping? Or is it only the GUI that does not work ?
ssh access is possible, but only if the machine responds to ping/ssh on one of the interfaces (obviously), if ssh is enabled in the remote debugging and if the ssh patch is installed. I am not sure if any of these three conditions is met in your case
If not, the only way I can think of would be serial access in the case of tha physical appliance, and the VMware console if this is a virtual appliance
Other than that there is not much more we can do. I would recommend a case be opened in support for this, as it will require further actions and analysis.