According to the specs of this PC you have an Intel Zeon processor and there is only one of them. No PC I know of has two CPU's, you may be confusing this with Dual Core, what you have is a variation of that. If one core of this particular CPU has failed I doubt the CPU would ever work.
Looking at your symptons I would first be checking the PSU, swapping it with another PSU would be a quick way to prove if the PSU has failed.
Do you get any beep codes when you try to boot?
One test you can try is to remove everything from the motherboard and disconnect all external hardware,keyboard, speakers, etc. Remove the Ram, disconnect all hard drives, any cards that are connected to the motherboard and CD drives. All you should have connected is the motherboard with CPU and cooler and the PSU. You should get a continuous beep when you switch on.