My iphone 5s had blue screen and now it wont turn on. How can i fix this?

My phone has been having blue screen for about a week and itll go blue and shut off, but when i did the hard reset (holding down home button and lock button) it would come back on but sometimes i would have to do it a few times for it to finally come on. So last night i tried to restore it with itunes but it wouldnt work so i unplugged it and it turned off. Now it will not turn on at all, the apple icon comes on as long as im holding the lock button but as soon as i let it go it goes away, and if i keep holding it then after 15 seconds it shuts off by itself. Please please please help me!

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