I have no clue how bad your HD is. Does it spin, what OS, make noise? ....come on give me some clues here.
If this is your boot drive, used to boot PC? Does it spins and make no noise, remove from PC and mount in an ext. USB case. -OR- or mount in another PC as 2nd drive. If damage is what??? You could possibility recover data that way, access files, etc., and xfer them over. You may get lucky and simply clone that HD to a some media.
OTHERWISE, you need the special services of some recovery outfit. Provided you can spare the cost and data is "priceless", do that NOW rather than attempt any self-recovery as you reduce your possible damage any further.
Regardless, of any googled info or YouTube success stories, each HD failure is unique and the less attempts at fixes may provide the fuller return of data. Understand, anything you do further is at "your own risk".
Check the "storage forum" here on CNET forums and find the "sticky"(top post) for pgms./apps that may help. Procedures and such vary but you need to learn as you go. good luck
recovering files from damaged hard drive