All those things, the start button, the eject function, and the on/off symptom involve the same part (the faceplate). To me, it sounds like you have a faulty or loosely connected faceplate ribbon. If it still doesn't work correctly after completely disconnecting the faceplate and its ribbon from the motherboard, try replacing the faceplate. It's easier to replace the entire faceplate than to replace only the ribbon. May God bless you and your family today! Xtreme Games Dallas
Reballing is not worth it for an Xbox 360 unless you do it yourself, but a reflow is less expensive and easier. If the reflow doesn't work, you need to replace either your motherboard or the entire unit insides (to keep your special edition shell). May God bless you and your family today! Xtreme Games Dallas