For some reason, some of the SharePoint servers could not connect to the SQL Server. Some of the servers did not have a problem. The previous day everything was working, and nothing changed.
I could ping and telnet to the SQL Server, but still had the error.
I ran the following command to clear out the ARP Cache. That fixed the problem:
netsh interface ip delete arpcache
Now that I mention it, the network department had some issues.... mmmm.