My laptop broke and I've heard that there are services that can save the data from the hard drive, but I don't know who offers such a thing.
You will quickly find enough companies on Google that do that.
But your hard drive itself will still be intact, so you can simply read it with another PC.
Do not believe that a professional data recovery is paid at 29.95 …
Just buy an external hard drive and backup your most important data on it. Next time. Otherwise, you can try using the Data Recovery Wizard to restore the data.
https://www.recoverylab.de/datenrettung-wiederherstellen/datenrettung-festplatte/
For example.
Google knows even more providers
First of all, it should be enough to remove the disk and connect it to another PC. If you don't think you can do it alone, there's sure to be a PC shop near you where something like this is done, or you google for "PC helfer" or "PC doctor" + your home town.
If the disk should actually have a major damage (head crash or similar), then google for data recovery + hometown, there are now a lot of professional companies. When my record had a head crash 15 years ago, this one got it
https://datenrettung.net/
The best thing to do is to do these services yourself.
If the laptop is defective, I assume that the hard drive is OK, that is, remove the hard drive and install it in an external housing and connect it to another PC.
First of all, it should be enough to remove the disk and connect it to another PC
Maybe as a little addition:
If the laptop does not have a screw-on hard drive slot and you are not very familiar with assembling hardware, you better go to a specialist.