[NumLock]

если создать пустое приложение:

Код:

unit Unit1;

interface

uses
  Clipbrd,
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, StdCtrls;

type
  TForm1 = class(TForm)
    Edit1: TEdit;
    Button1: TButton;
    procedure Button1Click(Sender: TObject);
  private
    { Private declarations }
  public
    { Public declarations }
  end;

var
  Form1: TForm1;

implementation

{$R *.dfm}

procedure TForm1.Button1Click(Sender: TObject);
begin
  Edit1.Text:=Clipboard.AsText;
end;

end.

будет работать?
и Clipboard.Open; && Clipboard.Close; не нужно, ибо:

Код:

function TClipboard.GetAsText: string;
var
  Data: THandle;
begin
  Open;
  Data := GetClipboardData(CF_TEXT);
  try
    if Data <> 0 then
      Result := PChar(GlobalLock(Data))
    else
      Result := '';
  finally
    if Data <> 0 then GlobalUnlock(Data);
    Close;
  end;
end;