Although I highly recommend not using the ISP DNS servers, I would set this by altering the DNS settings directly on the Weatherlink IP, because that then means that you are switching to a static IP on the device and you could end up with IP conflicts on your network if you don't also mitigate that on your DHCP server (typically on your router), where you would then set up an IP address reservation. Rather what I would recommend is to change your DNS on your router so that it propagates your custom DNS settings to all your devices on your network.
68.105.28.11 is Cox cable's primary DNS server. If the rest of the network devices are working then DNS is likely not the issue.
I would once again remove power and batteries from the console. Then ensure that the IP logger connection to the console is firm...disconnect and reconnect. Then return batteries and power to the console.