Port 10443 is the vCenter 5.x Inventory Service HTTPS port. Make sure the vCenter Inventory Service is running and shows a healthy state in the vCenter Server Status health section of the vSphere Client.
Did you separate vCenter components or is everything running on one server?
Can you open this link in a browser? https://vcenterfqdn:10443/ (or wherever you have your Inventory Server installed).
Also make sure there is no firewall prohibiting access to that port. Also open the vSphere Client from the vCenter locally to eliminate causes like this.