SQL Connection - Creating And Working With Database

On my development PC I have SQL Server installed, and my SQL connetion works perfect. I use a trusted connection. But on other PCs, where the program should work later, there is only a SQL "Express" installed (by another application), and it seems they have an password on the SQL Server (I guess). I have no chance to get the password from the other application. My connection is not working here. I created some connection test, but it does not seem to work with the trusted connection. I need the SQL only for creating my own database and connecting to my own database. So how do I create a connection with SQL Express for creating and working with my own database?

Here my code for testing the connection so far (Fehler means Error, erfolgreich means Success) Private Sub mnu_Verbindung_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles mnu_Verbindung.Click
Dim bolFehler As Boolean = False
Dim sServer, sDatab As String
[Code] .....