One can use below mentioned MS SQL DNS less connection string for ASP Script:
Dim SqlConn
Set SqlConn = Server.CreateObject("ADODB.Connection")
SqlConn.ConnectionString="Driver={SQL Server};" & "Server=MS SQL Server IP;" & _"Database=dbname;" & "Uid=username;" & "Pwd=password;"
SqlConn.Open
Response.Write "SQL Connection Successful"
Dim SqlConn
Set SqlConn = Server.CreateObject("ADODB.Connection")
SqlConn.ConnectionString="Driver={SQL Server};" & "Server=MS SQL Server IP;" & _"Database=dbname;" & "Uid=username;" & "Pwd=password;"
SqlConn.Open
Response.Write "SQL Connection Successful"