Resolving could not open a connection to SQL Server errors

Problem

Sometimes you may have issues connecting to SQL Server and you may get messages such as the following:

ERROR: (provider: Named Pipes Provider, error: 40 – Could not open a connection to SQL Server) (Microsoft SQL Server, Error:) An error has occurred while establishing a connection to the server. (provider: Named Pipes Provider, error: 40 – Could not open a connection to SQL Server) (Microsoft SQL Server, Error: 5)

Or

An error has occurred while establishing a connection to the server. When connecting to SQL Server 2005, this failure may be caused by the fact that under the default settings SQL Server does not allow remote connections. (provider: Named Pipes Provider, error: 40 – Could not open a connection to SQL Server) (Microsoft SQL Server, Error: 1326)

Or

A network-related error or instance-specific error occurred while establishing a connection to SQL Server. The server was not found or was not accessible.  Verify that the instance name is correct and that SQL Server is configured to allow remote connections. (provider: TCP Provider, error: 0 – No such host is known.) (Microsoft SQL Server, Error: 11001)

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