You can try plugging it in again to see if your phone responds to the power surge. You can also try the soft reset function - hold the sleep button and the home button at the same time for at least 10 seconds and see if anything comes up. Sometimes my screen doesn't display which can make it look like the phone isn't running, but for me, it has been, it just needed to be rebooted to fix itself. If that doesn't work and the phone is new, call up the place you got the phone and get it swapped on warrantee asap. The longer you wait, the more excuses they will be able to give you.
The same thing happened to mine. Required a new digitizer, however I just purchased the front panel assembly because I was not in the mood to use a heat gun to get the ear speaker and home button off.
If you just very slightly twist this plate clockwise as you are lifting it out, it will help as there is a little hooked piece at the lower edge on the very far right. You have to be careful not to turn it too much though because this hooked piece is right beside a ribbon that could be damaged.