Actually I have something very similar with my Xbox 360, once in a blue moon the Xbox 360 wont turn on, so I tried turning off/resetting the power bar and turn it back on ( I give it about 10 secs before i turn the power bar back on, but probably does not matter) and it fixes the problem every single time.
I probably has happened about 7 times and have owned the 360 for about 2.5 - 3 years.