You answered five minutes after I posted this question. Wow!
Using anything other than "XE" in the TNS Service Name in the ODBC Data Source Administrator causes the connection test to fail. I suspect that there might be something wrong in my ODBC Oracle driver installation. Will reinstall. And will try a 64-bit ODBC driver.
In the meantime I downloaded installed a MySql ODBC driver. With this I was able to connect instantly from QlikView to the MySql database. This gives me what I need to begin exploring QlikView.