iphone 5. black screen of death???

So i went to bed the other night and my phone worked fine. When i woke up the next morning, the screen was completely black. now that the screen is completely black, the vibrate button doesnt work. No Vibration, no noises. I cant hold down on the lock and home button to try to turn it off because my lock buttons broken. My lock button has been broken now for about 4 months but i just put on a setting which allows me to click on a button and lock my screen so i didnt get it fixed. My only solution was to let the phone die and then charge it and turn it back on. After 2 days, it finally dies. I plug it in and the charging icon comes up. I think to myself perfect, nothing is wrong with the screen or i wouldnt be able to see this image. So after it starts charging, it finally tries to turn on by itself. The apple icon appears as usual, then nothing. The apple icon has been up on the screen now for about 5 hours and still nothing. Here is the biggest and stupidest part of the story. I didnt back up my phone since ive owned it, and i have really important pictures and information i need to get off the phone. Is there anyway i can recover this information, or any way i can fix my phone???? It will also not respond when i plug it into the computer. PLEASE HELP!!!