Do you have root access to the server via the WebHost Manager and SSH? If you do not, or do not know what this means, you will need to contact your host for assistance.
If you do have root access, make sure the cpdavd service is running. Make sure it is enabled in Main >> Service Configuration >> Service Manager. Next, log into the shell and make sure that it is listening on the needed ports:
If there is no output, then nothing is listening. Try restarting the service:
# netstat nalp|grep 2077
# netstat nalp|grep 2078
You mentioned having the firewall disabled locally, but the server may have firewall rules in place that block the DAV ports, and the network that hosts the server may also have firewall rules. If you are the server administrator, please submit a ticket so that we may look at your configuration directly and help you resolve the problem.