관련 소스를 드리겠습니다.
저의 경우엔 Label과 Image컴포너트를 옮겼고
CSpinEdit를 이용해서 위치 확인을 했습니다.

참고하세요

bool IsDragging = false;
int OldX, OldY;

void __fastcall TForm1::lbCreditsMouseDown(TObject *Sender,
      TMouseButton Button, TShiftState Shift, int X, int Y)
{
    IsDragging = true;
    if (dynamic_cast<TGraphicControl*>(Sender)){
        Screen->Cursor = TCursor(crHandPoint);
        OldX = X;
        OldY = Y;
    }
}
//---------------------------------------------------------------------------
void __fastcall TForm1::lbCreditsMouseUp(TObject *Sender,
      TMouseButton Button, TShiftState Shift, int X, int Y)
{
    IsDragging = false;
    if (dynamic_cast<TGraphicControl*>(Sender)){
        Screen->Cursor = TCursor(crDefault);
    }

}
//---------------------------------------------------------------------------
void __fastcall TForm1::lbCreditsMouseMove(TObject *Sender,
      TShiftState Shift, int X, int Y)
{
    DragMouse(Sender, Shift, X, Y, seCreditsX, seCreditsY);
}

//---------------------------------------------------------------------------
void __fastcall TForm1::DragMouse(TObject * Sender, TShiftState Shift, int X, int Y, TCSpinEdit* x, TCSpinEdit* y)
{
    TGraphicControl* Obj = dynamic_cast<TGraphicControl*>(Sender);

    if(IsDragging && Obj)
    {
        Obj->Left += X - OldX;
        Obj->Top += Y - OldY;
        x->Text = IntToStr(Obj->Left);
        y->Text = IntToStr(Obj->Top);
    }
}