You can use a macro. The following macro will count all non-blank cells in
the (first) column in the selection. A message displays the result.

You do not need to select the entire column before running the macro. It
will check all cells even if you have only an insertion point or if part of
the column selected.

Note that the macro will consider a cell as non-blank even if the cell
contains spaces only. Additional code can be added to prevent this if desired.

Sub CountNonBlankCellsInColumn()

   Dim oCell As Cell
   Dim n As Long 'used as counter
   
   n = 0
   'Check whether selection is in table
   If Selection.Information(wdWithInTable) = False Then
       MsgBox "The selection must be in a table. Please retry.", vbOKOnly
       Exit Sub
   End If
   ‘Check all cells in the first column in the selection
   For Each oCell In Selection.Columns(1).Cells
       'Check whether row is empty - delete if it is
       If Len(oCell.Range.Text) > 2 Then
           'Cell is not empty - count
           n = n + 1
       End If
   Next oCell
   
   'Show message
   MsgBox "The (first) column in the selection contains " & n & _
       " non-blank cells."
End Sub

For help on installing macros, see:
http://www.gmayor.com/installing_macro.htm