So, it is possible to retrieve files from a formatted or wiped drive, right?
Possible, in theory. Reality can be a different story.
Sadly it's going to be a suck-it-and-see exercise.
The obstacles against you are going to be what has happened to your data since the Windows was reloaded.
HP wouldn't of just reloaded Windows, it would have done something to the drive first - a reformat, delete the partition, who knows.
Then Windows would have been reloaded from an image on the recovery partition, then the standard operating environment including all the crapware that HP offers.
Then, maybe, someone would have loaded their personal software, settings etc.
Each time the hard drive was written to, your personal data was made that little bit harder to recover.
I'm guessing the person who did the reload ignored the big 'Are you sure?' warning that hopefully HP would have displayed.
(excusable - we all make mistakes)
I'm also going to guess from this Recuva exercise, that there are no backups.
(inexcusable - that's just laziness)
And as a last kick in the guts, even when you find the files, and Recuva does it's magic, the files could still be corrupted, or at least in a state to be unusable.
Sadly it all comes down to how much activity has gone on.
But, fingers are crossed....