This specific error:
SQLServer JDBC Driver]Error establishing socket to host and port: ALMDB_TEST:1450. Reason: Connection timed out: connect
Is saying that it cannot connect on port 1460 to SQL-Server ALMDB_TEST.
Try using MS-SQL Server Management Studio to try to connect to your SQL-server FROM THE QC SERVER and login (as the QC DB Admin, or the ''td'' user). You could also try to establish an ODBC connection (Windows/Control Panel/Admin Tools/ODBC).
This will tell you if your QC Server can indeed reach the SQL-Server instance.
Check the port and password for the ''td'' user OR if using Windows authentication in SQL-Server, the user specified to run the QC service.
Sometimes when booting a QC server at the same time as the database server, QC will start BEFORE the database is ready, so it is best to give ample time to the DB startup, then start QC. If the DB is known to already be up and running, then this is not an issue.