Windows – How to recover data from crashed Windows laptop

I am surprised that running manually bcdboot against the ESP did not perform the trick; in fact, it could even been seen as a bug of it (meaning to be reported to Microsoft.) Are you 200% sure that you identified correctly what your firmware believes is the system partition?

The EFI system partition is not the only place to clean, the EFI variables (controlled by the UEFI firmware) could also be corrupted, particularly since you mentioned the BIOS reinstall had adverse effects. bcdedit /storeP:\ath\to\BCD\file\on\mounted\efi\part/import /clean (from the command prompt of the advanced options of W8 recovery) is the Windows' way to clean its cached copy, which copy is what you are really seeing on Windows boot manager screen; Linux offers, through efivars, even more powerful tools over them.

While you are here, follow Rod's advice and check thoroughly the output of bcdedit /storeP:\ath\to\BCD/enum all for unneeded or misplaced entries, which you could try to dispose of after having made a backup of the BCD file.

If you consider only Windows, the organization of the ESP is straightforward: besides the mighty Bootx64.efi, everything is under the \EFI\Microsoft\Boot\ directory. The only file you might edit is the BCD, through bcdedit. To be able to boot, you need just \EFI\Boot\Bootx64.efi, \EFI\Microsoft\Boot\BCD, and \EFI\Microsoft\Boot\boot.stl on the ESP, assuming the former is a copy of \EFI\Microsoft\Boot\bootmgfw.efi; keeping this later is a good precaution, particularly since you are considering the installation of other boot managers which could replace the mighty Bootx64.efi (but should generally left untouched bootmgfw.efi.) During the boot process, some (hidden) BCD.log* and BOOTSTAT.DAT files will be automatically created in \EFI\Microsoft\Boot\. You might also see \EFI\Microsoft\Boot\bootmgr.efi, although nobody seems to know what it is good for... The ll-CC directories with the MUI resources help to be able to display non-English messages instead, depending of the settings in BCD; similarly, the fonts could be needed for non-Latin cases; I found out that removing all this i18n stuff for cleaning purposes, did not help on the long run, since I use to turn them back in place, to get back my own language while booting.

Maybe it´s too late, but just in case... I have had the same problem: boot sector and its backup are different. But one of them is correct. The same tool you have used (TestDisk) allows you to save all the files in that disk whereever you want. It´s a very slow process (almost 30 hours for a 750GB disk) but I did save all the contents of my ISB drive.