You can use the Windows API function GetVolumeInformation()

procedure TForm .Button Click(Sender: TObject);
var
  VolumeSerialNumber : DWORD;
  MaximumComponentLength : DWORD;
  FileSystemFlags : DWORD;
  SerialNumber : string;
begin
  GetVolumeInformation('C:\',
                       nil,
                       0,
                       @VolumeSerialNumber,
                       MaximumComponentLength,
                       FileSystemFlags,
                       nil,
                       0);
  SerialNumber := IntToHex(HiWord(VolumeSerialNumber), 4) +
                  '-' +
                  IntToHex(LoWord(VolumeSerialNumber), 4);
  Memo .Lines.Add(SerialNumber);
end;