The only thing that comes to mind is that some laptops occasionally just lock up and can't be powered up or down without a complete removal of the power source. I've heard of some people who just let the battery run all the way down, and once it's drained to a certain point where it exits the lockup condition, it will recover and can power up when connected to the power adapter.
Not saying that it's what you're experiencing, but it's one possibility. I've had it happen a couple of times, and both times were slightly different. Once there was a faint electronic buzz telling me something was partly drawing power, but it was in some sort of weird state where the normal powerdown mechanism wouldn't work.
I can't tell you how to fix it if that's your problem, but I believe that Apple or an AASP can fix it fairly simply. I'd say get it evaluated and see what they say.