How can I still save the data? Should I take something out of here?
Naturally. Remove the HDD. RAM possibly. Also…
Removing the HDD is undoubtedly located under the large cover. You can build it into an external SATA USB housing and use it as an external hard drive. You can then transfer the data to a new computer, for example.
Does the laptop no longer show a picture or does it simply no longer boot?
Yes, there's also where the data carrier is.
You have to unscrew the maintenance cover, there should be the hard drive / SSD somewhere, which you either have to unscrew or can pull out.
What is no longer working on the laptop?
If necessary, this can easily be rectified again.
Otherwise, remove the hard drive (unscrew the lower service flap -> see YouTube videos) and buy a USB-SATA adapter.
With this you can connect the laptop hard drive directly to any other PC without having to install the hard drive there.