How do I fix the error Named Pipes Provider error 40 - Could not open a connection to SQL Server

Question

I can't seem to link from a site to my database. I experience the following error:

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

I tried using the local IP address to connect as well as a public one. I've tried:

1. Yes, the site can communicate with the server
2. Named pipes/TCP is enabled.
3. Remote connections are allowed.
4. Windows Firewall is off
5. Created an exception for port 1433 in Windows Firewall.
6. Enabled everything in SQL Server Configuration Manager.

What else can I do here?