[X 2014 Android Development] mikeoswego:
Both of the 7z files you uploaded are empty. Don't worry about that now. XDA doesn't like 7z files so better to use .zip (have 7z make a zip.)

The kmsg file is the kernel log, last_kmsg is the end of the kmsg log from before the last reboot. It only contains messages from the kernel and what you posted earlier kind of looked like some app or something commanded or caused a reboot and the kernel did as it was ordered. The system log is where all the apps and services will write there stuff to and it is huge compared to the kmsg log. Ideally, once you've got CatLog recording the system log and the phone reboots, you'll collect the last_kmsg and the recorded system log and match them up (although I think by now we're not going to see anything new or conclusive in the kmsg file.)

Do you have a USB-OTG drive to plug into the phone? If not, get one! :) Get one that has both the regular USB and micro USB for the phone and you can transfer files that way as well. Or get a cheap USB-OTG to USB adapter to use with your existing USB drive. Then with TWRP, you'll make a backup to USB-OTG. Note that TWRP does not backup sdcard or internal storage so you have to back that up separately to your pc via usb or to the USB-OTG drive by copying the files you want to keep such as your pictures, music etc. (Actually, it is possible to make an exact image backup of sdcard by using the command line in TWRP if you want to dedicate a USB-OTG drive for that purpose.)

Anyway, once you have that TWRP backup, you can get right back to where you were. This is how I switch back and forth between stock and the CM rom or do major experiments fearlessly. You can make modifications to /system or even delete everything and use TWRP to restore just the system partition to where it was when you started.

Maybe some or all of this is irrelevant.. If something is found in the system log that looks fishy, that app can be uninstalled or disabled and see if the problem goes away. If nothing looks suspicious or it is some system process that has screwed up, the chances of fixing that without wiping data or even formatting data are pretty slim.

The original factory rom no longer exists in your phone. The only rom you have is in /system. If you backup it up with TWRP, you can restore it. If you've never modified it, you should be able to just reflash it with TWRP or using the mofo version if you still have that. You've seen Windows computers where the only thing to be done was reinstall and that happens with Android too. It's a pain to redownload all the apps and set everything up but it does clean out all the accumulated garbage to wipe /data and start fresh. Presuming you've let your contacts be backed up to your Gmail account it isn't all that painful. The last time I did this Google automatically dl'd all my apps and restored some settings.

Make your TWRP backup, wipe data and cache in TWRP advanced wipe, reboot, let Google restore your contacts, setup just the minimum apps and see if the phone works or not. Even without a backup as long as you don't wipe system, the currently installed rom will stay installed. You've probably spent way more time trying to fix this then it would take to just setup the phone again. :p