My HDD is a mess, doesn't boot, doesn't mount. Anything I can do, except formatting?

Hi guys, this is my first post in any Linux related forums, so please be kind. So my problem is, as stated in title - I cannot do much with my HDD. I don't really know any cool commands to type in terminal to fix my issue, I did google around, tried Code:fsck in many different variations, but nothing seems to help me. I would really like to fix this HDD without formatting it, as it contains data that I need.

I was running Lubuntu, all was fine, but one time it just wouldn't boot -- it kinda boots, but screen stays black where the login screen should be. What I have done now is, I have booted Live Kali from USB stick.

I know it is not much information, but im ready to provide all information necessary, if anyone would point where to look for it!

Thanks to anyone even reading this!