I actually had this problem with mine, and I guess I'm one of the lucky ones, so far... *knocks on wood*.

I got my 770 last week. Charged it over night. When I first plugged it in I noticed that the screen powered on and displayed a charging icon. I slipped on the cover and let it charge with the screen de-activated.

In the morning, I tried to power it on, but it appeared to be dead. I remembered that the screen had been on the night before, so it couldn't be completely dead. I tried to power it up again, pressing all the buttons, holding the power button for 20+ seconds, connected and disconnected the Power supply, removed and replaced the battery, etc. Finally it powered on, but I had no idea what the trick was.

For the rest of the day, it was very difficult to power on during the several times I did so, but somehow I got it to start up each time.

At night I flashed over the stock firmware with the latest one, and I've yet to experience the same powering up difficulties again.

In my case I'm inclined to conclude that it is (was) a software issue.