As long as you don't overwrite the deleted file by saving a new file on top of it, you can typically recover it. I've had very good success with Paragon EasyRecovery Pro software
. I've recovered things as simple as an accidentally deleted file to stuff from hard-drives that were formatted and re-partitioned.
Here's the process I would use:
1. remove hard-drive with data to be recovered from computer and put in safe place (like a vault).
2. install new hard-drive into computer
3. load clean Windows OS
4. install Easy Recovery Pro software
5. re-install old hard-drive as secondary data-drive on computer
6. run recovery software and scan entire data-drive, may take a couple hours
7. sort through list of files and pick the ones you want to recover
8. save recovered files to different drive than original, perhaps a USB disk to bring them over to new computer.