In your case the best bet would be a data recovery firm. If the HDD is dead you will not be able to get the files by yourself. They can open the HDD up and actually transfer the platters on a different drive. Or it could be the controller, although that is not very common with HDD. Mechanical parts fail sooner than electronic parts. That being said, it is not impossible for it to go the other way around.
Either way, if taking the HDD out and mounting it inside a PC does not fix the problem, the HDD will need to be deconstructed by a specialized firm.