Hi!
I think the problem of yours is because the over heat in some part of the motherboard and/or another device.
As " brutalspoon" said, the over heat of CPU is not responsible for a such problem, also the capacitor would discharge quickly -not couple of days!-.
My friend has a little similar problem, that his computer shut down by itself without an alert, then he found an IC in his motherboard was getting over heat quickly and cause a shut down, and after about hour -until that IC cool down- the PC would turn on properly, and he had to change this IC with another healthy one.
Then, be sure that the temperature your PC in, is cool and in its operation temperature limits, and at last try to remember when and after what you have done, the PC became a CRAZY!!
Bye!