Why does my macbook always shut down on recovery?
Boot the Mac from a known-good local OS.

You can install an OS on to USB drives (HDD, SSD, flash) or even set up a local net boot server, but you'll need to get logs of how far into the boot process the computer gets to diagnose what subsystem is failing.

A hardware technician might remove all of the components that are not needed to boot the system and ensure that the RAM and logic board are working, but I wouldn't recommend starting hardware diagnosis before you've finished the software analysis and brought a known good OS of a proper version for your Mac to the suspect hardware.