One obvious question is HOW the laptop got "broken". If you dropped it, especially while it was still running, it's very likely you damaged the hard drive in the process.
If you want to try to recover some files from the hard drive, you may be able to do that with a data recovery app. I recommend RecoverMyFiles only because I've used it. It might be able to find recoverable directories and files -- and you can install and try it for free -- to see what it finds. You have to purchase it (on line) to do the actual file recovery.
I don't know of any way to "get around" formatting it that will not "erase" the existing files and directories.
