Find the forums that was published at and you find the "How to use Odin" pages. I don't get into that here since it's done at their site and well done too,
My answer is to ask the carrier to reflash the phone.
My S4 wanted to install an update: before letting it proceed I thought it would be good to backup - however after/during backup (Kies 3/Smart Switch on Windows 10) something happened, and now it fails to boot fully - just ends up on a constant boot cycle, almost as if the system update was run but corrupted.:
1. get the Samsung splash screen with the model number, followed, eventually with
2. the Samsung colourful graphics "fireworks" which stop, and then the phone Vibrates/buzzes twice, and then restarts,
3. GOTO '1' - repeating itself continuously.
Manage to get a recovery logo by using Power+VolUp+Home, and releasing power at logo. When I do this the device goes straight into a "installing system update" with Droid wiggling ears, then appears to crash out of that with "no command" and comatose Droid animation and return to the familiar faulty boot/cycling behaviour.
When I was backing up, Kies had reported,
Current version: PDA:OJ2 / PHONE:OJ2 / csc:0J1 (BTU)
Latest version: PDA:PK2 / PHONE:PK2 / csc:PK1 (BTU)
Size: 1458 MB
Don't seem to be able to do much else (hard reset or wipe cache). I think I can get into download mode - Someone suggested using Odin or Kies to re-flash the device with stock firmware, which sounds about right.
Network unlocked phone - sim on monthly with Three / Hutchinson network UK.