Try this in a copy of your actual workbook, not the original...
Sub PasteRange()
Dim wb As Workbook
Dim wsSource As Worksheet
Dim wsTarget As Worksheet
Dim r As Range
Dim varVal As Variant
Dim lngRow As Long
Set wb = ActiveWorkbook
Set wsSource = wb.Worksheets("Sheet1")
Set wsTarget = wb.Worksheets("Sheet2")
Set r = wsSource.Range("A1

13")
wsTarget.Activate
Range("A1").Select
varVal = ActiveCell.Value
Do Until varVal = ""
lngRow = lngRow + 1
varVal = ActiveCell.Offset(lngRow).Value
Loop
r.Copy
wsTarget.Paste Destination:=wsTarget.Range("A" & lngRow + 1)
Application.CutCopyMode = False
Set wb = Nothing
Set wsSource = Nothing
Set wsTarget = Nothing
Set r = Nothing
End Sub