The Automated Patch process seemed to have hung up and we restarted the database and core servers. Thereafter we were unable to log on to the consoles.
The associated error logs are attached for reference.
Based on the error reported (10060) the incoming rules on the Windows Firewall on the Database server were re-checked. The SQL Management Studio rules allow TCP and UDP connections on all ports for local and remote connections. (The SQL Native Client configurations also appeared correct). Because of the error a new rule was created to allow TCP 1433 for the domain and private networks and after creating this rule the customer were able to log on to the LANDesk Management console on the Core server.