Motherboard has power but CPU won't turn on

so my computer would randomly turn itself off after some time without being used, however the other morning when I went to turn it on, my processor fan turned on for a split second but then stopped, I know the motherboard has power because the little green light is on, as are all other lights that would be on without hitting the power switch. any ideas?

The power supply has died. Just because you see green lights doesn't mean the power supply is supplying all the voltages needed by the computer. It could also be the motherboard, we'll go for the power supply first

thanks, I thought thats what it was, just wanted another opinion and it was right