Hi,
I am having the same problem with my Macbook Pro 2011 model. The gist of it is this. It turns on sometimes and sometimes it just doesn't bother to. The sleep light either keeps blinking or shines, then dims.
Currently, it has turned on and now I am afraid to turn it off. Even went to the Apple service center. Those people diagnosed it as the fault of the logic board which I don't think is the case. I am not willing to spend so much on a good-for-nothing machine anyways.
But, I just want resolutions to my problems. Otherwise, I think I would have to sue Apple for selling me a product with a manufacturing defect. Urgent help needed. Please help me!