Mac starts to boot up and then shuts down

Try nvram reset. If that doesn't work you could also try using verbose mode as a boot arg. With computer shut down, boot into verbose mode by holding down the command key and the v key immediately after you press power button. It should flash the error message at the bottom of all the text (probably the last line but could be several before the final line) right before it shuts down (or could hang instead of shutting down) so you may need a cell phone to record a video to be able to read the error message being shown. You can also repeat the process in safe mode plus verbose mode by holding down command + v + shift at the same time after pressing power button.