I'd recommend doing a factory reset, and if it doesn't work - take it in to a local repair center or the store at which you bought it.
Unfortunately with the system not booting, you won't be able to back any of your data up. However everything on the SD card will be untouched, and the contacts should be synced with your Google account.
Make sure it's off and plugged in to power.
Press and hold volume down + power until a menu appears. The menu is not touch capable, you can navigate using the volume buttons and the power key. Find the option for factory reset and confirm that's what you want to do.
Let it do it's thing, it should only take about five minutes.