It might be the power supply unit

I had the same problem for my old P4 machine. It has 4 HDDs on it. The machine works fine for about a year, before I don't use it everyday. After a year or so, it can't be started! I think PSU is deteriorating.

It turns out one HDD is having problem as well, as it requires some extra current to start. If I use only one HDD, the PSU works fine!

Well, I can live with one HDD and didn't bother to change my PSU.