Q: i just baught an iphone 4 for my daughter it has a new battery and back put on but after her having it for couple of hours the screen went blank thought it was dead when pluged into charger logo stayed on and phone vibrated then nothing

my iphone 4 went blank today thought it needed charge so when pluged it in logo came up but didnt go any furthure, so connected it to itunes through my computer and when doing restore an error 11 came up i dont know why can this be fixed? only got the iphone for my daughter for xmas and only used for couple of hours and this happens. the phone is second hand and has had a new battery and black put on by apple..