I was having this problem where I couldn't even get to a screen with apps and such and I noticed there was no solution here so this is what worked for me 🙂
5S Blue Screen Crash After iOS 8.1 Update
Problem: Since upgrading to iOS 8.0 my iPhone 5S randomly gets blue screens and then crashes and goes into a loop of boot up, blue screen, reboot, blue screen, reboot…etc. My 5S did this again today when during my upgrade to iOS 8.1 via USB and I was forced to do a factory restore on it. The blue screen is still occurring after the restore and 8.1 upgrade. Is this a known issue? I was hoping this was going to get fixed with 8.1 but unfortunately, it doesn’t look like it has.
Solution: You will have to use Recovery Mode to restore your phone in cases like this. To place your phone in Recovery Mode follow the steps below. Make sure to back up your data first.
- Turn off your device and leave it off.
- Plug in your device’s USB cable to a computer with iTunes.
- Hold down the Home button on your device as you connect the USB cable. Keep holding down the Home button until you see the Connect to iTunes screen.
- When your device is connected, iTunes will open. You’ll see a message saying that iTunes has detected an iPhone in recovery mode.
Restore your phone using iTunes.
http://www.studentnewsie.com/fix-common-iphone-5s-problems-ios-8-22433