So, on Tuesday my computer failed to power up - drives and fans were spinning, but no power to USB, no POST beeps, black screen. And it was a while since the last backup. Panic.
Quick googling told me that the PSU is the most common reason for such problems and it rarely takes the hard drives with it. Yesterday I installed a new PSU and everything was fine again: no other component seems to be broken, and most importantly, no apparent data loss either, the HDD worked without problems. First thing to do was of course to run a new backup nevertheless.
Thank the Maker that nowadays even ready-made PC's use standard components that you can easily replace yourself. As long as you have a tabletop model, that is, and that is why I'll never buy a laptop myself.