IPhone 5 Doesn't Want To Turn On

Last week I restored my iphone 5 and I also updated it, it worked normally but the only problem was that battery was dying pretty fast. After charging it I turned it off and after a day when I tried to turn it on again it just didn't want to do that. I thought that battery died, I tried to charge it but there was no signs of charging, I tried turning it on, even pressed home button and power button but nothing was appearing, it was completely dead. Earlier I took it to this store and tried to change the charger and also to check if it was the battery but even after that phone stayed dead. I don't know what could be the problem. I tried everything. I can't turn it on, power-home button is not working obviously, when I try to connect it to itunes it doesn't recognize it at all (like it is not even connected), I tried changing usb and battery and still nothing.