Sounds like you already took some good troubleshooting steps, then. Did you happen to have tried it with the drives unplugged from both the PSU and the motherboard? If it started but shut down after about five seconds, then I'd also suggest maybe the power button is having a mechanical problem and remaining "pushed" internally, but it sounds like it shuts off faster than that.
If it's got a slot-1-style CPU, also re-seat the CPU in case it got jarred loose a little. If all else fails, try stripping the mobo bare (not even the CPU itself) and then start it that way. The power supply's fan should start running and stay running, if the motherboard is healthy (although it may let out a fussilade of beep codes). If that doesn't work then you can try it with another PSU to judge whether the PSU is dead. Good luck with the troubleshooting