Problem connecting to SQL Server 2008 over local connection

I just had SQLServer2008 installed on a computer with Vista Home Premium SP1.  I added a test database with one table and two fields in the table.  

I am trying to test the connection from another computer in our office.   I am using a vb6 program that connects fine to remote SQL Server (I don't know the version number).  The connection string that works for the other SQL Server is:   Provider=sqloledb;Data Source=xx.xx.xx.xx;initial Catalog=mydbname;User Id=myusername;Password=mypassword;

I've tried several variations of connection strings and none of them have worked.

Right now, with this connection string:   "Provider=sqloledb;Data Source=EXCELSS-PC\SQLEXPRESS;Initial Catalog=myTest;User ID=Excelss;Password=popcorn;"

where EXCELSS-PC is the computer name.

I"m getting the following error:

Run-time error '-2147467259 (80004005)':

[DBNETLIB][ConnectionOpen (Connect()).]SQL Server does not exist or access denied.

I am guessing that I'm either using the wrong information for datasource, username, and password . . .or there is something going on with the security on the windows side.   From 'Network', I can see EXCELSS-PC and if I double click on it, I can use the username and password above to get to the shared resources (only the printers folder).

Any thoughts?

Dim cn As adodb.Connection
    Set cn = New Connection
 
    cn.ConnectionString = "Provider=sqloledb;Data Source=EXCELSS-PC\SQLEXPRESS;Initial Catalog=myTest;User ID=Excelss;Password=popcorn;"
 
    cn.Open

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