It is always best to completely log out of the GUI environment when running a full system update, and to update your machine from the command line in a tty instead. That way, no shared libraries will be in use that are about to be overwritten by the update process.
Never switch off your machine or hit the reset button in the middle of a full system update. The update process first downloads the packages to /var/cache/pacman/pkg/, and then begins replacing the packages on your system, whereby the first thing it does is remove the to-be-replaced kernel images and initramfs from /boot. It is only at the end of the update procedure that the new kernels are installed, the initramfs images for these new kernels are generated, and GRUB gets updated.
If you shut down or reboot your machine in the middle of an update, not only will you have no kernels and/or initramfs ─ which means that there’s nothing left that can boot your machine ─ but you also stand a chance of damaging the filesystem and losing your files.
The update process does not touch your BIOS or UEFI. If your Num Lock light is flashing, then that means you’ve got a hardware error, and it may very well be this hardware error that caused your system to crash in the first place. And if you then add that your graphics hardware is fried, well, then there’s the culprit.
I’ve had a dying onboard GPU die on me in my previous machine, and it made the machine unusable. I had one crash after the other, and especially when doing GPU-intensive things like watching a video or using compositing effects.
I’m afraid your machine has just given up its ghost.