Connection string and backup operation

Question

Hi,
I am a programmer Italian, I do not know English well. I hope to explain my problem well.
I develop in C # on a PC with Windows Seven Pro, vs 2010 pro, sql server 2008.
I have problems with the backup operation and the connection string.
The code is as follows:
private void BK()
  {
  string strconn = @"Data Source=.\SQLEXPRESS; AttachDbFilename=|DataDirectory|\db.mdf;Integrated Security=True;User Instance=True";
  SqlConnection conn = new SqlConnection();
  conn.ConnectionString = strconn;
  try
  {
  //Query per backup
  string queryBK = "BACKUP DATABASE db TO DISK ='C:\\Program Files\\Microsoft SQLServer\\MSSQL10.SQLEXPRESS\\MSSQL\\Backup\\db.bak' WITH INIT, SKIP, CHECKSUM";
  //Creazione Command 
 
  SqlCommand cmdBK = new SqlCommand(queryBK, conn);
  // Open connection.
  conn.Open();
  //Execute command 
 
  cmdBK.ExecuteNonQuery();
  MessageBox.Show("backup effettuato");
  }
  catch (Exception ex)
  {
  // Process exception.
  MessageBox.Show(ex.Message, "ERRORE", MessageBoxButtons.OK, MessageBoxIcon.Error);
  }
  finally
  {
  conn.Close();
  }
  }
This code works on the development PC, but if I install my application on another PC (with Vista) does not work, returned the following error:
"The database does not exist. Verify that the name has been entered correctly. INTERRUPTION
 ANOMALOUS BACKUP DATABASE."
I would stress that this string works well with the operations INSERT, DELETE, UPDATE
on both my PC and on the PC test.
If I replace the connection string with:
string strconn = @"Data Source=.\SQLEXPRESS; Database = db;Trusted_Connection =True";
The string work on my PC but on my test computer returns the following error:
"Can not open database requested by the login. Login failed.
 Login failed for user Pina-PC \ Pina "
Someone could help me to solve this problem?
 Thanks...Iole