Thank you andrewb, PhoenixAwakened, and vikon.
All my problems are solved for now. Actually it was my own doing. From that grub calamity that broke down both my systems and I reinstalled on both of them, I was so afraid to do a system update, as all the hell broke loose from that innocent ‘yay -Syu’ and both the machines were booting into bios again and again like a Myth of Sisyphus.
And now, emboldened by your suggestions, dear friends, I did it on both the laptop and the desktop and they are working fine. This forum is really nice.