The error suggests you cannot connect remotely, so first step is to connect to the database through SQL Server Management Studio locally.
There are three things you can check.
The first is that the TCP/IP service is enabled (you've done that already.)
The second is that remote connections are enabled. To check this, right click on the database server in SSMS and choose properties. Then go to the connections tab and ensure that the "Allow remote connections to this server" is checked off.
Finally, you have to make sure that the firewall on the SQL server machine is allowing inbound connections on the SQL server port (1433). How to do this is dependent on what firewall you have installed.
Also important to consider:
Is SQL server running on a different server than SharePoint, and can SharePoint access the database? If both of these are true, than it means that it is possible to access the database remotely, so the next place to look would be why you personally can't connect.