My second monitor went dead this morning. No standby light, nothing. The easy answer is a new monitor, and the slightly-less-easy answer is a new internal PSU board off a marketplace for a tenner. But before either of those I did the thing that is almost always worth doing first: I opened it up and looked.
It took about four seconds to spot. One electrolytic capacitor on the secondary side, 1000µF, with a domed top where a flat top should be. Swollen, sometimes a little crusty round the vent. That is the classic failure: the cap dries out, bulges, and the rail it was smoothing gets noisy enough that the supply refuses to come up. It is the single most common reason cheap consumer kit dies, and it is the easiest to fix.
The repair is genuinely trivial if you can solder. Note the polarity, the stripe is the negative leg, desolder the old cap, drop in a replacement of the same capacitance and voltage rating (or higher voltage, never lower), and match the temperature rating at 105°C. Mine cost about forty pence from the drawer. Powered it back up and the standby light came on like nothing had happened.
I am not pretending every dead device is one capacitor away from life. Plenty are not, and mains-side faults deserve respect and a discharged supply before you go poking. But a bulging cap is a five-minute fix and a perfectly good monitor saved from the skip, and I would rather spend the forty pence and the solder than the tenner and the guilt.