Can you hear the fan running at all?
Try connecting an external monitor to the laptop’s HDMI port and check if there is a display showing on it at all when you turn on the laptop.
If there is a display showing then you can use the external monitor so that you can “see” how to transfer your data, in the usual manner, to an USB flash drive or USB HDD connected to your laptop. You cannot transfer anything to a monitor, it is just a display unit, not a data storage unit.
After this you can attend to the problem of your laptop screen not working.
If there is no display on the external monitor or the laptop is not working at all then there may be a problem with the GPU or the motherboard.
You can always remove the SSD (Solid State Drive) from the laptop and connect it to another PC as a secondary drive. Search online how to install a laptop SSD (or HDD same principle maybe different connector types) in another PC to recover data from the SSD
Here’s a link to the service manual for your laptop. Scroll to p.40 to view the necessary pre-requisite steps and then the procedure to remove the SSD.