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.