iphone 5c turns on then black screen

hi, my phone had 3% of battery when i decided to charge it, when i plugged the charger the big red battery logo appeared so i figured that the battery died, so i left my phone charging, after a couple minutes i went to check on it to see my messages, and it was all black so i pressed the on/off button, the apple logo appeared so i waited for it to turn it on, it was taking longer than i thought so i checked again and when i pressed the home button it was all black like it was turned off, i repeated all the process of turning it on and waiting and it still appeared the black screen, i don't know what to do! and i don't want to restore it because i have important pictures in it and stuff like that. So please help me. thanks, mariana