First thing to try, take your xbox part, really all you need to do is take out the hdd caddy, and unplug the yellow wire that goes through the metal heat sheild in the front of the xbox. Then when that cord is unplugged plug your xbox into the wall and see if it powers up.
Sometimes the buttons on the power/eject board wear out. I've seen this problem before so more than likely it's your power/eject board.
For a long time it gave me nightmares. Having to witness an injustice like that. It was a constant reminder on how unfair this world can be. I can still hear them taunting him. "Silly rabbit trix are for kids" How come they couldnt just give him some cereal? (Before you post)(Download my cheater C)
There is a thread about this very problem on llamma forums.. It's back about 2 years ago but a moderator should be able to point you in the right direction.
It's related to leakage between tracks on the mobo and sometimes a failed chip. (one of the original chipset, not anything later fitted)