Problem with timestamp code

I'm trying to trigger a timestamp when certain cells are filled in a spreadsheet. The code I'm using works fine when entering one cell at a time, it doesn't work when I paste multiple cells. Any ideas?

Thanks much!


The code:

Private Sub Worksheet_Change(ByVal Target As Range)
Sheet1.Unprotect
For Each Cell In Target
If Cell.Column >= 2 Then
If Cells(Cell.Row, 2) <> "" And Cells(Cell.Row, 3) <> "" And Cells(Cell.Row, 4) <> "" And Cells(Cell.Row, 5) <> "" And Cells(Cell.Row, 6) <> "" And Cells(Cell.Row, 7) <> "" And Cells(Cell.Row, 8) <> "" And Cells(Cell.Row, 9) <> "" And Cells(Cell.Row, 10) <> "" Then Cells(Cell.Row, 1) = Now
End If
Next Cell
Sheet1.Protect
End Sub