|So nothing at all shows on the screen and no beeps? Not that it'll fix anything but if you hold the power button down for 4 - 5 seconds it will shut down.|
Did anything happen to it or did you make any changes between the last time it worked OK and the first time it didn't?
Not to be too general but, depending on the answers above, it's the power supply motherboard or both or, less likely, something connected to the motherboard.
You can start by removing the power cord, opening the case and disconnecting all the drives and removing any add-on cards except video (if you have a video card). Then plug it back in and start it up. If you get the system logo or posting screen then one of the removed items must be at fault. If it's still dead then you're back to it being the power supply, motherboard or both. (Both, since when a power supply fails it often ruins the motherboard as well.)