Oh, I absolutely have a love affair with a program called Easy Recovery. Several years ago and I do mean several since my computer at the time was only a few years old and the hard drive still under it's warranty, my HD started failing and like you I was told to reformat, but I also know that the first thing these stupid tech people will tell you, without telling you that you stand to loose everything. Nor will it solve the problem if the equipment ain't worth the gigabyte it's supposed to hold. Anyway, I knowing a wee bit more then the tech support, decided not to go that route and started looking for ways to recover the files first. Like you I had photos that I'd taken with my 35mm that I just scanned and really wanted to save. So it took a few weeks but I finally found something and yes I put out the money for it after I ran a demo version and it found the files I was trying to save.
It was downloadable then, I don't know how they sell it now. But it still should be. Anyway, Easy Recovery was made by OnTrack Data International at the time. I don't think Ontrack has it anymore, so you may have to fish round a bit to see who publishes the program now.
Ontrack programs work, because they work outside whatever OS you're running and are not limited to that program standards. There are a couple of ways to recover files using ER and one of them is RAW reading, meaning that it will read any and every inch of your hard drive to find even the smallest amount of information and if it's found give you back a recovery option. The first method is done by sector reading outside the OS, it's reads the File Allocation Table.
It will find anything there. Sometimes the files are so badly damaged it can't be recovered so it won't even give it a usable name, but it will report it in it's finally report.
The only thing I may see you having a problem using this, is you cannot recovered to the drive that it's reading from. The program will recover the files, but you need to have someplace to put the recovered data. Like an Zip Drive, an External HD, and since you're using a Laptop, probably you're computer's HD will do, but it's something ER has to see as another HD. Depending on the size of your Laptop HD, if you already have logical partitions of your actual physical drive, you can save the data to one of the partitions.
Example, like me when I recovered mine files, I had one 20gig drive, I then created 2 other partitions on the same drive, of different sizes and different formats. So, I reduced my C drive, which was the main drive to 10gigs and created one 2gig partition that could read DOS programs strictly and one 8gig partition for storing and running my FAT32 stuff. Giving me a C, D and E drive and someplace to store the data that ER would find and recover for me.
That was the best software money I've ever shelled out. The other thing, it's time consuming, both in terms of how long it takes the program to work and how long it takes for you to sort through the stuff you recover. If the data is outside the OS the files will not have the same names they were originally saved with or given. So you literally have to view every single file recovered to find what you're looking for. Oh the extension will likely be the same, but just not the first names. But if the data is that important to you it's more then worth it.