Thanks for your question.
Sorry for your troubles.
Yes, your data should be recoverable.
Off the top of my head here are two of a few ways you can get your data:
One: If you can get your hard drive out of the laptop and put it into an external hard drive chassis, you could plug it into another computer and save it there.
-This is for those comfortable pulling apart a laptop or pc. Hardware solution.
Two: If you can make yourself a "live bootable usb drive" for a linux operation system then you will have no issues finding your data on your laptops hard drive and saving it off to a thumb drive or external hard drive.
-This is for someone comfortable with diving into a new operating system. Software solution.
I realize that the solutions can be as, if not, more confusing than the question itself but that is where your research on the issue will come into play.
The main issue told by the error message. It soulds like iether your bios is missing something. Or the operating system is missing something.
The bios is the part of your software that starts working right after you press the power button. It checks the pc to make sure stuff like it's hard ware is working correctly. (Processor, RAM, Display, fans, and the like) It also boots the operation system. As in bringing up the windows logo before you get to your desktop.
If it is your opperating system that is missing something you should still be able to get your data back with the soulutions above.
The computer doesn't touch the hard drives information (which is where YOUR data is also stored) until a little bit before you actually see the windows logo during start up. So it should be there still.
The only way that your data WON'T be recoverable is if it's the hard drive itself that is damaged. Then I'm sorry to say that thers not going to be much that you can do to get those 1s and 0s back.
If you are not comfortable with tackling this on your own, try to find someone that is savy enough to the Data Recovery. Payment is up to you for the service. It's whatever the data is worth to you.
Oh, and if the only answer you're getting is to do a factory reset as "the only way," then it's of my professional opinion that this person is not trying hard enough to find solutions for you. (No offence of course to whom that is. Lol.)
Hope this helps.