Phone won't turn on

Hi,

My Iphone 5s is not working any more. I didn't upgrade to IOS8 and all was working fine. Then I started to get a blue screen and the phone would restart on its own, when this happened a few times I decided it was time to upgrade to IOS8. While I was upgrading the phone got blue screened and it shut down and now it is non-responsive. It won't turn on, I plugged it to an electric socket and tried to turn it on and I still don't get any response. I took to the apple store and my warranty expired 2 months ago (I know my phone was getting blue screens before than date but they can't turn the phone on to check the log when the errors began). Please help. Thanks.