It could be a few things - firstly (I know this sounds stupid) make sure all cables are plugged in. If they were, next... unplug everything other than power, keyboard and screen
From what you have said, I would assume the error is either with the Power Unit, Motherboard or graphics card.
(I have read Aaron's answer - possible hard drive, but unlikely. It sounds like it is powering up then going to safe/standby. Your machine should boot, just come up with an error if it was the hard drive.)
(Only if you have a beeper/speaker) We can quickly see if the motherboard is dead - Try to unplug the memory - start up and if you hear a beep code (no memory) then the motherboard should be good. If you do not hear anything, the board may be dead, but you can try a few other things.
If you don't have a beeper/speaker, start here:
If the motherboard has internal graphics, I would next try plugging directly in there or using a different graphics card as we need to diagnose if the problem is with that.
If you do not have any way to test the graphics and have an internal beeper/speaker, you can try just unplugging it all together - if it is able to proceed with boot (e.g. one beep), it means that the problem was with the graphics.... however you have to remember if the board beeps on boot, and also, not every machine boots without some sort of graphics output.
(left in the above to help others, I have seen your motherboard does have internal graphics).
If there is no speaker, or alternate graphics card to test, it is hard to proceed.
However, if you get an image through the internal graphics, then the problem was with the graphics card.
If you do not get an image, the problem is either either the power unit or motherboard.
I would try unplugging everything other than PSU to motherboard. This includes optical and hard drives.
If you are able to boot, the power unit is not outputting enough power to all devices and you need a new (possibly more powerful one).
If you are not able to boot, most likely (in my experience) the motherboard has gone, however you still can not rule out a faulty PSU.