Ok the problem has been solved
Code:
 Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click
        Dim con = New SqlConnection("Data Source=.\SQLEXPRESS;AttachDbFilename=C:\Users\Danial\documents\visual studio 2010\Projects\ESI_PF_Payroll_V1\ESI_PF_Payroll_V1\Pay.mdf;Integrated Security=True;Connect Timeout=30;User Instance=True")
        Dim adaptor As New SqlDataAdapter
        Dim dataset As New DataSet
        con.Open()
        con.Close()
        If Firstname_txt.Text = "" Then
            MsgBox("Firstname Cannot be blank!")
        ElseIf Lastname_txt.Text.Trim = "" Then
            MsgBox("Last name Cannot be Blank!")
        Else
            con.Open()
            cmd = New SqlCommand(str, con)
            cmd.Connection = con
            cmd.CommandText = "SELECT * FROM Employee where Firstname ='" & Firstname_txt.Text.Trim & "' and Lastname ='" & Lastname_txt.Text.Trim & "';"
            cmd.Connection = con
            adaptor.SelectCommand = cmd
            adaptor.Fill(dataset, "O")
            Dim count = dataset.Tables(0).Rows.Count
            If count > 0 Then
                MessageBox.Show("This Employee Does Exist!")
                Dim str, str1 As String
                 str1 = "Select Employeecode from Employee where Firstname = '" & Firstname_txt.Text.Trim & "' and Lastname = '" & Lastname_txt.Text.Trim & "';"
                cmd = New SqlCommand(str1, con)
                cmd.Connection = con
                dr = cmd.ExecuteReader
                While dr.Read
                    Empcode.Text = dr(0)
                End While
                con.Close()
                con.Open()
                str = "SELECT SUM(Present) FROM Attendance WHERE AttendanceStatus = 1 And Firstname = '" & Firstname_txt.Text.Trim & "';"
                cmd = New SqlCommand(str, con)
                cmd.Connection = con
                Dim _dr As SqlDataReader
                _dr = cmd.ExecuteReader
                While _dr.Read
                    TextBox1.Text = _dr(0)
                End While
                con.Close()
            Else
                MsgBox("This Employee does not Exists!")
                Firstname_txt.Text = ""
                Lastname_txt.Text = ""
            End If
        End If

            con.Close()
    End Sub
Now the sum is also correct against the First name and the Last name ,and also solved the Shaggy Hiker and a Shaggy Runner thing.
Thank you all for guiding me and helping me to solve this issue.many more to come hehe .