Problems turning on Iphone 6

So here's what happened to my Iphone 6 (64 GB) phone. Updated to IOS 8.4.

For a while, it's been giving me a scrambled screen. And when I tried to turn it on sometimes, it just gave me a blank screen (not white). It used to work after I turned it off and on repeatedly.

One day (today), it stopped turning on. It just gave me the blank screen that it usually gave. I connected my phone to my mac and opened Itunes to restore it, but it said that I needed to turn off "find my Iphone" (but i couldn't since my phone won't turn on.) So I decided to hold the home button and the standby button together for a while. After I did that, my phone turned off. Now it won't turn on. I don't know what to do. And i have a lot of valuable information on my phone that i really don't want to lose.

You might ask me if I backed up my Iphone. I did, but I have a lot of new information which I need that aren't included in the back up.

I need help ASAP pls!