Iphone 5s stuck on black screen with apple logo

My phone has been playing up for a while now, for example the other day it deleted ALL of my messages, every time i delete i turn my phone off it erases all my messages i had, my apps crash all the time, i have no memory no matter how much i delete and my iphone battery is VERY BAD.

Today it just crashed and has been stuck on a black screen with the apple logo which has a bar underneath it. I have plugged it in for hours and still no luck. i cant turn it off. I cant press the home button and turn off button at same time as my home button is broken. I can connect it to itunes as i have a pass code on my phone and it wont turn on. im on the verge of tears right now as my phone isnt backed up and i have ALOT of precious photos that will be erased.