Are you able to get into Safe Mode using the steps listed in this document?
If so,you may be able to backup your files manually using your preferred method. Read the section "Recover your notebook" in its entirety within this document. The recovery will provide an option to perform a backup, but it is an automated process and I cannot guarantee it will get everything you want it to as it will only backup what it finds.
Furthermore, you could use something like Ubuntu to backup your files. Just be sure to disable secure boot in BIOS and enable Legacy Mode. BIOS can be accessed by powering it on and pressing F10 about once a second.