Dropped iPhone, now its acting up

So, i dropped my iphone 5s [that i got brand new last week from at&t] around 8 hours ago. the screen is super shattered from the corner and i think i stepped on it, so there are too deep dent on the bottom of the gold metal backing, above the white panel, and a long dent across the top of the gold.

fast foward to 20 min ago, my phone shut off as if it died but didn't light up with the little spin dial thing. it was at 100% too so it definitely wasnt a battery life. i pressed and held the lock button to turn it back on; the blck and wite screen popped up and then turned black again in like 3-4 sec. i held the home button and lock button for 6-10 sec.; nothing. so i plugged it into the wall charge, ad the black/white apple screen came on and stayed on and went to my regular lock screen. battery was at 100% still so i was like, ok weird.

Then it turned off again, so i tried to plug it into mylaptop and it would try to turn on and light up the b/w screen but then would turn black, so i plugged it into the wall, it turned on [with the battery at 1%??] , then i plugged it into the computer. itunes responded to it and the phone responded as well, so i backed it up.

now it's turning off and on, and before it turns off, a blue screen rolls down from the top and then it turns off. its still plugged in to the computer cause i'm trying to restore it as a new phone, but itunes says it's gonna take 3 hours to download the thing.

i'm already also in the process of going throught the at&t insurance thing so yea

will all these software problems happen when i get my new phone? is the backedup software corrupts from this or is this all from the physical damage and maybe where the dents are?