Iphone 5 randomly gets blue screen. Will not turn on after I tried to restart it.

I have had my Iphone 5s since about a month after they came out. It has worked perfectly up until now.

While I was at work I was going about my regular business using my phone as usual. I put it into my pocket and about 15 minutes later pulled it out to check it but all that was on the screen was a dim dark blue light. I couldnt do anything on the screen including turning it off so I did that hard reset (holding the Home and Sleep button).

After the phone shut off it did not turn back on. I tried every combination of buttons and reset options.

-(Home/Sleep buttons)

-(Home/Sleep buttons +Volume up and down)

-(Home/Sleep buttons while turning the mute button on and off)---This one was just a theory online, same as the one before it.

-(Restored the iphone multiple times in itunes)

I had the phone plugged in for a good amount of time and while it was charging it would periodically do a quick 2 vibration burst, like it was starting to connect.

Im guessing its just not getting past a point in the restarting process so it just doesnt continue, seeing as it is still accepting a charge (Itunes put it at 68%)

Anyone have any theories or explanation as to why this could be happening? I appreciate any response

Thanks