The machine had been getting flaky on cold starts. Press the button, fans twitch, nothing. Press it again and it'd come up fine. Classic dying-PSU behaviour, and the easy answer is to bin it and buy a new one for thirty quid. But it was a decent unit, out of warranty by years, and I had a soldering iron and an idle Saturday, so I opened it up first.
You can usually spot it by eye. Three of the electrolytic capacitors on the secondary side had domed tops, the little crimped X bulging upward instead of sitting flat, and one had the faint crusty residue that means it's been venting. Capacitor plague, basically, cheap caps that don't survive years of heat. Mains side first: unplug it, leave it sat for a good while, and discharge the big primary cap through a resistor before you go anywhere near the board, because that thing will absolutely bite you long after the lead's out.
The fix is unglamorous. Desolder the three bad ones, note the voltage and capacitance printed on the side, and put in fresh 105°C-rated parts of the same value. I had a couple in the drawer and bought the rest, total damage under a tenner. Watch the polarity, the stripe is the negative leg, get it backwards and you'll find out with a bang.
Buttoned it back up and it's cold-started every morning since without a sulk. Not every PSU is worth saving and not every fault is this visible, but bulging caps are the most repairable failure in the box, and it's a genuinely satisfying twenty minutes with an iron. Beats landfill, too.