help splitting text files

Good morning everyone, I am trying to create a small application, (VB.NET 2003) for breaking larger text files into smaller ones.  The files need to be exactly 60,000 rows in length and the last file created amounts to the rest of the data.  For example, the original file has 190,000 rows and is named tempfile.  My desired result is the creation of 4 new files.  The first three have 60,000 rows in each and the last file has the remaining rows of data, (10,000 rows).  Also if possible I would like the files to keep the name of the original file and add a –part to the output files.  In the above example the result was the creation of four new files.  I would like them to be named tempfile-part1, tempfile-part2, tempfile-part3, tempfile-part4.  Another thing is that I never know how many rows are going to be in the files and I know they have been as large as 3 million rows.

Please see the commented sections of my “attempted” source code below.

Thank you very much for taking the time to read this post and for any technical advice you can help me with,  
Gr8life

Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click
        Dim inFile As String
        Dim outFile As String
        Dim openFileDialog1 As New OpenFileDialog

        openFileDialog1.InitialDirectory = "c:\"
        openFileDialog1.Filter = "txt files (*.txt|*.txt|All files(*.*)|*.*"
        openFileDialog1.FilterIndex = 2
        openFileDialog1.RestoreDirectory = True

        If openFileDialog1.ShowDialog() = DialogResult.OK Then
            inFile = openFileDialog1.FileName
            outFile = Mid(inFile, 1, inFile.LastIndexOf("."))

            'Need help creating the process of naming the files the OriginalFileName-part1, OriginalFileName-part2, etc
            outFile += "-part1.txt"

        End If

        Button1.Enabled = False
        Dim startDT As DateTime = DateTime.Now

        If (inFile.Length > 0) Then
            If (outFile.Length > 0) Then
                ConvertFiles(inFile, outFile)
                Dim stopDT As DateTime = DateTime.Now
                Dim elapsedTS As TimeSpan = stopDT.Subtract(startDT)
                Dim msg As String = elapsedTS.Hours & "h" & elapsedTS.Minutes & "m" & elapsedTS.Seconds & "s"
                MessageBox.Show("File Complete! " & ControlChars.CrLf & ControlChars.CrLf & "Process Duration:" & ControlChars.CrLf & msg)
                Button1.Enabled = True
            Else
                MsgBox("No output file specified!")
            End If
        Else
            MsgBox("No input file specified!")
        End If
    End Sub

    Public Sub ConvertFiles(ByVal filein As String, ByVal fileout As String)
        Try
            If (IO.File.Exists(filein)) Then
                Dim sin As New IO.StreamReader(filein)
                Dim sout As New IO.StreamWriter(fileout, False)
                sout.AutoFlush = False ' output file is NOT updated after every WriteLine() call
                Dim lineCounter As Integer
                Dim items() As String
                Dim readline As String = sin.ReadLine
                While Not IsNothing(readline)
                    items = readline.Split(vbTab)
                    sout.WriteLine(String.Join(vbTab, items))
                    lineCounter = lineCounter + 1
                    If lineCounter Mod 60000 = 0 Then
                        'sout.write I am having trouble creating the files based on the row count
                    Else
                        'sout.write the remaining data to the last file
                    End If
                    readline = sin.ReadLine
                End While
                sin.Close()
                sout.Flush()
                sout.Close()
            End If
        Catch ex As Exception
            MsgBox("Problem Occurred" & ex.Message)
        End Try
    End Sub