There's usually there's a code that is displayed along side a blue screen, THEY_LOOK_LIKE_THIS. If you an take a note of that and let us know we might be able to help with a repair.
If you remove the HDD and buy a [https://www.amazon.co.uk/s/ref=nb_sb_noss_2?url=search-alias%3Daps&field-keywords=sata+to+usb|sata to usb cable] you won't need to pay someone to recover the data.
As for the laptop, I'd let it go, get a new one.