I've only had my Galaxy Tab 2 7" for a couple weeks, but I've had the same exact problem occur twice.
I charged my GT2 overnight about a week ago, in the morning I unplugged it and hit the power button to wake it up, but it stayed blank. I pressed the power button for a couple of seconds like you would when turning it on, and it still remained blank. I had to hold the power button in for considerably longer than you normally would to get it to turn on. When it turned on, everything was normal.
The same thing just happened to me now, only I wasn't charging it. I used the GT2 and then pressed the power button like I normally do to put it to sleep and then placed it on my coffee table. An hour later I came back to use it and it didn't wake up when pressing the button. The same thing happened when I pressed it for a couple seconds as if I was turning it on from being shut down, it still remained blank. Finally I pressed the button for about 7-9 seconds and it started up like normal.