This may sound obvious, but did you charge it? Also, there is an issue sometimes where auto brightness turns the screen all the way down. Try shining a bright light on it to see if you can see anything.
Also, try holding the power button, and both volume up/down at the same time for at least 10 seconds.
The SAME thing just happened to me. Get my new Nexus 7 2013 home from Staples, charge it fully, and it won't turn on. I am SO pi$$ed! The thing is going back tomorrow morning - I want a different one, and if it doesn't work - I'll leave Nexus forever. Hello, Samsung Note!