One can use below mentioned MS SQL DNS Based connection string for ASP Script:
Dim SqlConn
Set SqlConn = Server.CreateObject("ADODB.Connection") & _
SqlConn.ConnectionString = "Provider=sqloledb;" & "DSN=sqltest;Initial Catalog=databasename;" & "User Id=username;" & "Password=password"
SqlConn.Open
Response.Write "SQL Connection Successful"