I had the same problem too. I operate a Mac Pro Early 2006, but it just can't start up after a long sleep. When I pressed the power button, it seems starting but then just buff off. I've taken all hdds and rams and let the machine running with just os Hd and it seems to be going. I've tried installing the unplug hardware and seems to be working. Another option i normally tried also, which helped to me due with start up issue is a preRam reset by, cmmd, opt together with P and R key, all pressed down after you hear the first chime, and still pressing it till you hear the second chime then released the keys.
But I think i might be agree with dxhole, commenting on the power supply. It could be the source of the problem.
Hope to hear any further comments on this folks..