My initial thought is the top case has a sticky power button, but strangely enough the trackpad can also affect this. I've had an off and on battle with systems that will reboot when you press the power button instead of powering off, and starting semi-spontaneously... Long story short, finally traced it to a bad trackpad on at least one system. At least as soon as I disconnected the trackpad, suddenly things started working. Best I can figure out on this, the trackpad and power button cables tend to be right next to each other, so maybe some crosstalk on the signal pathways.
This is something I would recommend taking it somewhere to get looked at, because odds are they're going to have to replace something. A local AASP or Apple store, doesn't really matter.
Hello- I have so far had a few instances of this phenomenon w/ my 15 mo. old Mac. First, when charging my Mac at night in off-mode, it will occasionally turn itself on at some point evidenced by the power-on when it's opened. Then,I have had one instance of a shut-down by itself during use. It restarted w/ no problem. Next, the computer turned itself on with the cover closed and the computer had been off all night. I heard it start up, so I am sure. Any ideas? I do have AppleCare if I need to take it in. Thanks- Sobergirl05

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