If the failed drive is the C: drive, then this method probably won’t work unless you have other hard drives on your system. The setup program needs somewhere to load the files in order to get to the recovery options. It is still worth a try, as the setup program may pick up one of the other disks and use that.
There are physical methods of attempting to recover a stopped drive too. Two of these are what I call “The appliance of violence.” They may seem extreme, but remember the drive is made up of moving parts. These can jam and prevent the drive from spinning or the head from reading or writing.
The first method is to remove the drive from the case and drop it. Not from a height, but enough to jar it. Then reattach it and see if it spins up. If that doesn’t work, get yourself a hard object, I use a screwdriver and smack the drive on the top, roughly in the middle. A good firm smack, not trying to take it out, just free up the internals in case they are jammed.
Older disks can develop sticking problems where a weak motor or tension between the platters and the heads can cause it to lock up. Either of those methods have been known to free them up and allow the drive to continue working.
There is another, more controversial method of freezing a hard drive. This is to force the different metals within the drive to contract. As these different materials contract at different rates, it can apparently free up locked drives. Of course once frozen, and warmed up, it is going to condensate, so it might be wise to attach it outside of the PC, retrieve data if it works then turn it off to dry thoroughly.
On the opposite side to that, an old IBM trick was to use a hair dryer on the failed drive. This worked on the opposite theory to freezing it, the metals expand when heated which can allow it to release any stuck heads or platters.
