O computador deve eliminar a carga estática residual, mas às vezes, em condições anormais, isso não acontece. Devido a isso, a placa-mãe se protege desligando-se. Isso explica os sintomas que você descreve: ventiladores girando, mas sem POST, o que significa que a energia está chegando, mas a placa-mãe não funciona.
Suponho que, se você deixar o computador sozinho por algum tempo, o problema será resolvido por si só, mesmo através das luzes LED. No entanto, pressionar o botão liga / desliga descarregará instantaneamente qualquer energia armazenada na PSU e livrará a carga estática.
O seguinte tópico expressa isso bem:
On an old AT type power supply, your procedure doesn't mean diddley. Nobody (well ok, very few people) use AT power supplies any more. Now we use ATX power supplies, which have some smart circuitry in them which is always on, even when the computer is off. Your TV is the same way. Most of the computer (or TV, or stereo) is actually powered off, but there are small circuits in there which are active which are used to sense when you want the device turned on, and they turn it on. Your procedure insures that these little circuits are completely powered off, and goes to the extra trouble of discharging all of the capacitors in the power supply to make sure that they aren't powering the circuits inside your computer too. Capacitors store energy, kind of like a battery. They are used in computers to smooth out variations in the power supply and keep things stable. Even when you turn something off, the capacitors inside it are still charged, and may have enough energy in them to power the really low power circuits inside for quite some time.