Phones don't normally require being turned on to charge them so there may be something wrong with your phone. Try these first and if it does that again within the first 2 weeks then take it back to the store.
remove the battery from the back of the phone, this will automatically turn off the phone so that you can pop the battery back on and just plug it in to charge it. Don't turn it back on yourself. If it turns itself on when you plug it in there is something wrong. If it just says "charging" that's fine, it is supposed to. If it actually boots up and you can see the signal indicator and your carriers logo etc on the screen then it turned itself on. First charge (always on a house charger, not car charger) should be about 8-12 hours.
Hope this helps.