Symptoms

Database server shows as Not Connected in Tools and Settings > Database Servers

Unable to access database via Webadmin:

A network-related 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: Named Pipes Provider, error: 40 - Could not open a connection to SQL Server)

or:

myLittleAdmin Silent Logon Error
A network-related 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: SQL Network Interfaces, error: 26 - Error Locating Server/Instance Specified)

MSSQL server name is different. On SQL Server Management Studio the name is:

.\\SQLEXPRESS

On Plesk > Database Servers the name is:

127.0.0.1\\SQLEXPRESS

Cause

Wrong username or password specified

Resolution

1. Get the correct username in SQL Server Management Studio login screen.

2. Update psa database:

   mysql> update databaseservers set host='.\\\\SQLEXPRESS' where id=x;