If the controller on the board has gone bad, there is no fixing it short of replacing the motherboard. The cable can be replaced, but I'm not an expert on laptops, so I'm not familiar with what you have. It is possible for a cable to stop functioning properly on a desktop.
Since the drive works in another computer, you've ruled out one possible problem. If the drive doesn't show up in the bios, then you have a hardware problem along the lines I've been talking about.