Network Access SQLExpress

I am  trying to access a SQLExpress database on another computer on my LAN.  Using Windows Authentication. I don't really want to go to Mixed Mode authentication as I understand it involves a registry tweak and creating a new user. I am a novice at this.

Getting the following error on running the connection code below:

SQLException was unhandled "Login failed for user 'D37YKC1SGuest'."

No doubt it is a security problem but I am not sure how to get around it.  Any help appreciated.

Connection code:

Dim conn As New SqlClient.SqlConnection

conn.ConnectionString = "Server=D37YKC1SSQLEXPRESS;Integrated Security=True;Database=VBNMDATA"

conn.Open()

Tried the following which is my Windows logon on the other computer (blank password) but same error:

conn.ConnectionString = "Server=D37YKC1SSQLEXPRESS;Integrated Security=True;Database=VBNMDATA; User Id=Geoff; Password="

I have TCP/IP enabled in SQL Express  and the firewall is off.  I can see the server on the other computer with this code:

Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click

' Retrieve the enumerator instance and then the data.

Dim instance As SqlDataSourceEnumerator = _

SqlDataSourceEnumerator.Instance

Dim table As System.Data.DataTable = instance.GetDataSources()

' Display the contents of the table.

DisplayData(table)

End Sub

Private Sub DisplayData(ByVal table As DataTable)

For Each row As DataRow In table.Rows

For Each col As DataColumn In table.Columns

MessageBox.Show(col.ColumnName.ToString & " " & row(col).ToString)

Next

Next

End Sub