It is broken and needs to be repaired, or replaced. If you know the battery has a full charge, and a battery pull doesn't work for you there isn't all that much you can do to fix it.
This problem is going to persist. Take it back today and get a new one. Even if it does turn back on eventually, it is a brand new phone and it shouldn't be acting like that.
Mine did the exact same thing last week. I went to Verizon and they sent a replacement, it arrived two days later. Verizon said the charger port looks to have broke on mine? I would say bring it in asap.
