It could be the power supply but it's very likely a motherboard issue. Your computer is still turning on the proof is in the fan working.
1st - I'm assuming you don't get any video on screen. If that is the case do you use a seperate video card or do you use onboard video? It could be that your computer is turning on and that you have a bad video card. If you use onboard video then you have a bad motherboard.
2nd - Does the computer beep at all when you turn it on?