Hey guys,
I had a similar problem and got it fixed combining the tips above.
What happened was last night I sent my laptop to sleep and charged it. This morning the screen wouldn't come on. The battery was probably charged because the power indicator light was white, but whenever I pressed the power button for two seconds, it flashed white 6 times. Nothing happened after that.
I couldn't force it to reboot either by pressing the power and home buttons.
So I did the down and power button twice and then home plus power button. Finally something showed up on my screen, it said the battery is 85% charged and the the screen went away just like when it was off. So I pressed the power button for two seconds and it finally woke up!