Original symptoms point to possible emmc failure, but since the phone is off warranty no harm in trying a few things.
Information so far:
1 - phone stuck at boot screen unexpectedly with no triggering change event noted (i.e. new app installed, or change to OS, etc)
2 - Power+Home+VolUp sends you to "failsafe" download mode, rather than recovery
3 - in Odin, status screen reports no pit partition
#1 alone given the timing, might suggest a botched OTA to 4.4.2. Adding in #2 and #3 tends to support the emmc failure scenario, however.
The i317m pit file is availble at this thread
You can try flashing it along with a custom recovery like twrp or philz cwm. I recommend this approach first rather than a full stock firmware - faster and will get you at least a working recovery for futher testing, error reporting and ability to wipe.
I typically use Odin 3.07 so if you use 3.09 you'll need to adapt these instructions a bit:
1 - put the pit file in the pit section
2 - check the "re-partition" box
3 - put the recovery tar or tar.md5 file in the PDA section (do not put a zip file here).
4 - click start.
5 - copy the contents of the message /status section back here when done.
Hopefully it works and you can use the power+home+VolUp combo from a powered off state to boot the phone into recovery.
If this result doesn't happen, you can try again flashing a param.bin + tz.img package, but we'll need to track down one specific to the i317m and the version of Android that was running on the phone before the problem started. (A bit of a long shot, but I've seen it work in the past).
Assuming no reconfig attempt brings it back, the hardware options are:
A - logic board ($175) or emmc chip ($150) replacement
B - phone replacement ($200 to $250), or less if you go with a different phone
(For option A I looked at mobiletechvideos.com pricing)