Hard-drive data recovery

With a mac you can dd an image of the entire disk to another hardrive using the diskutils under settings.

...and doing that will put the disk under severe load, finishing it off for good.

(Duplicating a disk will rarely solve a read problem and is not the best approach and it will crudely "stumble" over the data, ignoring any fragmented table allocations or partial data.)

they move all the info you want from your computer to their separate thingy

It sounds as if you went in with a corrupt OS install and they simply accessed your drive remotely, a failed HD (or HD with unreadable data) cannot be read from another computer unless there is simply a software problem or (non-HD) hardware problem on the original comp.