Same problems here with my iPhone 5s.
Whone hen the phone was on iOS 7 all was good but as soon as I updated to iOS 8 I started to have the problems. I've reset/restored etc numerous times both with USB connections and over the air Wifi and no joy. I've tried disabling the emoj keyboard, tuning auto brightness off and all sorts of different options I've found on various sites,l including setting up as a new phone and not restoring just in case there was something in the backup I am restoring that is causing the problems and nope, it's definately iOS 8.
the phone is consistent with its problem, there is no intermittens issue, it is the same each time and I do not believe its s hardware;
1. Touch home key to 'wake phone up'
2. Slide slider or finger print access to 'log in'
3. Within 10 seconds or so the screen 'freezes' with the exception of the very bottom of the screen where the dock is
4. Press power button to'sleep'
5. Press power button or touch home key as per #1 above
6. Same as #2 above
7. Phone is usable and I can use it until the battery runs out without any issues, but if it goes to sleep for more thank a brief period, such as >2mins (I've not timed this to be able to provide an exact time and if it's consistently the same amount of time each time) then I have to go to #1 above
very frustrating although I can get the phone into a usable state after faffing around, so I'm in a much better position than others by the sounds of things; not being able to take calls would be the end of it for me as I rely on my phone for my business so I sympathise with you about this, is it a contract phone that you can lean on your operator provider such as EE?
if you want to try a reset/restore and you know you have a backup on iCloud it is actually very easy, as I've done a couple of restores on an iPad in the last couple of days using the same process. Just send the phone into DFU whilst connected to iTunes, do the reinstall of software and then when it's done, log in to the phone, setup wifi and choose to restore from iCloud; ignore the message in iTunes at the 'set up as new phone' screen.
just hope Apple fix this in 8.1.3 as they must know about this even though they are not talking 😟