The possibility of recovering your files depends on the kind of drive failure: Soft or hard.
In case of a soft failure, where file structure is lost, you can recover files. In this case, most, and maybe all, should be intact.
There are many file recovery applications available, with free offerings available.
You can look on download.com.com (no typo, it's realy .com.com) or filehippo.com, both offering tons of free and virus free softwares.
Download and install a file recovery application.
DISABLE any smart defragmenter that can defragment your drive in the background.
Install the faulty drive as a secondary drive in any desktop computer.
Launch the file recovery application and analyse the problem drive. This can take a few hours to a full day depending of the size of the drive and the number of files present.
The recovered files WILL include many file fragments of older, deleted, files.
SAVE any recovered file to ANOTHER drive.
Finaly, check the recovered files to see if they are still usable.
Some of the recovered files can be corrupted, while others can be left over from deleted files. When you delete a file, the file is never actualy ereased from the drive, it's only flagged as deleted and it's location marked as free.
For the photos and other files that your niece created: If she shared some, she can ask her friends/family if they still have a copy and to send a copy back to her.
Then, there is the hard failure, or fault in the drive mechanism itself or it's logic board.
This can be a drive that no longer spin, the heads could be stuck, some broken wiring or the ciruit of the logic board could have fried.
In this case, you can probably no longer access even the raw data on the drive. It makes file recovery impossible, or so costly that you just can't afford it.
And, yes, as Alexander said, you should keep a copy of your files somewhere. At least the important ones and those that would be hard to impossible to find again. It can be an on-line storage (the so called cloud), some external drive, a bunch of DVD-R, some pen or thumb drive ...
Electro
December 2013