The PrintScreen system key is not processed during the TForm keydown event. The following example tests if the PrintScreen key has been pressed by calling the Windows API function GetAsyncKeyState() during the Application.OnIdle event. Example:

type
  TForm  = class(TForm)
    Button : TButton;
    procedure FormCreate(Sender: TObject);
  private
    { Private declarations }
    procedure AppIdle(Sender: TObject; var Done: Boolean);
  public
    { Public declarations }
  end;
var
  Form : TForm ;
implementation
{$R *.DFM}
procedure TForm .FormCreate(Sender: TObject);
begin
  Application.OnIdle := AppIdle;
end;
procedure TForm .AppIdle(Sender: TObject; var Done: Boolean);
begin
  if GetAsyncKeyState(VK_SNAPSHOT) <> 0 then
    Form .Caption := 'SnapShot';
  Done := True;
end;