The DCOM config test worked properly. The linked server QODBC shows up in Management Studio. When I run a query, I here the "Windows beep"  and the query  "SELECT ListID FROM QODBC...Customer" never finishes executing.

The queries do finish executing, but they never return any rows. I have gone through the entire setup process as described in the link you posted. Everything seems fine. In the VB Demo, the queries work fine. In SQL Server 2005 Express, the query executes successfully, but 0 rows are returned. I've tried many types of queries, but I always get 0 rows returned.

To be clear, the table header information shows up in Managment Stuio Express when I execute a query, but zero rows get returned.

Most likely you are using VB Demo and Management Studio at the same time. The QODBC optimizer is single user only so you need to setup a different optimizer file for the SQL Server to use than the other disktops applications. To do this step up a seperate System DSN (see: How do I create or configure a QODBC DSN? ) and specify a fixed location of the optimizer database folder for SQL Server to use instead of the default UserProfile method.

Also, please try running:

SELECT * FROM QODBC...HOST

as it's a one rowset table.

I was not using the VB Demo and Managment Studio at the same time. However, I have completed the steps that you suggested. I reloaded all data, but when I run the query

I here the "Windows beep" and it says "Executing query..." ,  but nothing else happens. I no longer get the table headers returned without rows.  

I have set up a separate DSN and optimizer file location. Am I NOT supposed to "Rebuild All Data" for this separate SQL Server optimizer file?

The table's column headers show up, but still zero rows are returned. I am using this query

Select * from QODBC...HOST

Please review the instructions shown at: Does QODBC work with MS SQL Server 2005 Linked Tables?  Try checking the "Run 2.1 ODBC Compatibility" off if it's already checked, or check it if it's currrntly unchecked.