The error message I finished last week with told me that the name pipes weren't working. That was still the case this week. It's irritating because I did the vanilla installation of everything and accepted the defaults. Honestly, I think that should guarantee success.
However, I have won this battle. I started reading the help to learn about this pipes business. It turns out that, by default, MSSQL listens on the pipe named\\.\pipe\sql\query unless you change it. But, the configuration program named the pipe \\.\pipe\MSSQL$SQLEXPRESS\sql\query Why? Because it's dumb. Also, I read about connection strings and, of course, they include the pipe name unless it's default. I figured that Visual Studio, since I have not told it anything about pipe names, would be trying to connect on the default. Solution: I renamed the pipe to be the default and, bingo, it works in Visual Studio. Now, what can I do with that connection? That battle is engaged.
UPDATE, 6/27/10: Doing this requires accessing:
Start->Microsoft SQL Server->Configuration TOols->SQL Server Configuration Manager
Then, in the left column click on
SQL Server 2005 Network Configuration->Protocols for MSSQLSERVER->properties
This will open a list of protocols in the right pane.
Double click on Named Pipes Properties and you will see a place to enter the Pipe Name (and enable it).
That's easy, right? I hate these people, even all these months later.