Append Text Files To Workbook

I want to open multiple .csv files from a single directory and append them to one workbook. The following code partly works, but appends only the first line from each file.

Sub GetFiles()
Dim w As Worksheet, fn As String, k As Long
Application. ScreenUpdating = False
Set w = ActiveSheet
k = Cells(65536, 1).End(xlUp).Row
If Not IsEmpty(Cells(k, 1)) Then k = k + 1
fn = Dir("*.csv")
While fn <> ""
Workbooks.OpenText Filename:=fn, Origin:=xlWindows, StartRow:=1, _
DataType:=xlDelimited, TextQualifier:=xlDoubleQuote, ConsecutiveDelimiter:=False, _
Tab:=False, Semicolon:=False, Comma:=True, Space:=False, Other:=False
Rows(1).Copy w.Rows(k)
k = k + 1
ActiveWorkbook.Close False
fn = Dir
Wend
Application.CutCopyMode = False
End Sub