The connection was not closed the connection's current state is open

I assume that the error is raised on this line:

con.Open(); // InvalidOperationException if it's already open

since you're reusing a connection and you probably have not closed it last time.

You should always close a connection immediately as soon as you're finished with it, best by using the using-statement:

public void run_runcommand(string query)   
{
    using(var con = new SqlConnection(connectionString))
    using(var cmd = new SqlCommand(query, con))
    {
        con.Open();
        // ...
    }  // close not needed since dispose also closes the connection
}

Note that you should not use a Catch block just to rethrow an exception. If you don't do anything with it don't catch it at all. It would be even better to use throw; instead of throw ex; to keep the stack trace. https://stackoverflow.com/a/4761295/284240

Better you write finally block and within it con.close() every where where you used try catch blocks. Eg.

public void run_runcommand(string query)   
{   
    try   
    {   
        con.Open();   
        SqlCommand cmd1 = new SqlCommand(query, con);   

        cmd1.ExecuteNonQuery();    
        con.Close();    
    }    
    catch (Exception ex)
    {
       throw ex; //TODO: Please log it or remove the catch
    }
    finally
    {
       con.close();
    }

}


try       
{           
    string query="my query";           
    db.run_runcommand(query);          
}         
catch(Exception ex)            
{         
    MessageBox.Show(ex.Message);              
}   
finally
{
   con.close();
}

Check the connection state before opening it:

if (con.State != ConnectionState.Open)
    con.Open();