your missing step 8
1.Prepare the new database server.
2.Close all open SharePoint Management Shell windows.
3.Stop all services that are related to SharePoint 2013 and Internet Information Services (IIS).
4.Detach the databases from the current SQL Server instance.
5.Copy or move all files that are associated with the databases (.mdf, .ndf, and .ldf), to the new destination server that runs SQL Server.
6.Make sure that all of the SQL Server logins, fixed server roles, fixed database roles, and permissions for the databases are configured
correctly on the new destination database server.
7.Attach the databases to the new destination server that runs SQL Server.
8.Use SQL Server connection aliases to point to the new database server and update all web servers.
If you do not want to use SQL Server connection aliases use one of the
following procedures to update the database connections for your
SharePoint 2013 farm.
◦Scenario 1: Use this procedure to update the database connections if
you use SharePoint Server 2013 with Service Pack 1 (SP1) and SQL
Server AlwaysOn Availability Groups for high availability or disaster
◦Scenario 2: Use this procedure if you do not use SharePoint Server
2013 with Service Pack 1 (SP1) and must use manual steps or if you
move the databases from a SharePoint Server 2013 single server
installation to a new single server installation.
9.Restart all services that you stopped in step 3.
for aliases connection do:
1.This procedure must be performed on all servers in the SharePoint Server 2013 farm that connect to the instance of SQL Server that hosts
2.Verify that the user account that is performing this procedure is a member of the following:
◦The Administrators group
◦The db_owner fixed database role
3.Start the SQL Server Client Network Utility, (cliconfg.exe). This utility is typically located in the C:\Windows\System32 folder on
Windows Server 2008 R2 Service Pack 1 (SP1) and Windows Server 2012.
4.On the General tab, verify that TCP/IP is enabled.
5.On the Alias tab, click Add. The Add Network Library Configuration dialog box appears.
6.In the Server alias box, enter the name of the current instance of SQL Server.
7.In the Network libraries area, click TCP/IP.
8.In the Connection parameters area, in the Server name box, enter the new server name and instance to associate with the alias, and then
click OK. This is the name of the new server that is hosting the
SharePoint 2013 databases.
9.Repeat steps 3 through 8 on all servers in the farm that connect to the new instance of SQL Server.
in your case i presume its an uptodate version for your db and sharepoint so do senario 1 or 2 as they ustalize powershell.