Stuck on bootloop, but I feel Stuck with All solutions I've tried, Help Please

[CheetyPants]

It started out of nowhere a few weeks ago, but got completely suck in boot loop a few days ago.
I've removed the battery and sim and sd cord and have let it sit, same issue.
I've tired using Odin 3.09 to reinstall to stock 4.4.2, then update from sd card to 4.4.4, still loops.
I can get into manual mode by holding the Volume up button, and I can get into download mode, holding Volume Down button.
I can't boot into Safe mode at all.
When I have my sd card inserted, I get no Blue Samsung "Swirl", just black screen and reboot, but after I wipe cache partition I get Half a "Swirl" then Reboot
the only thing I haven't tried is Wipe Data/Factory Reset as I have Files I wanted to keep, and hadn't Backed up in a while.

Any suggestions at all?

I can Deal with a factory Reset but, if I still get a boot loop, What then?:-\:'(

 

[CheetyPants]

Strangest thing just happened, I charged My Phone to 100%, turned it on, it's factory reset now but it's on, bitter sweet Victory?

 

[caseym54]

Is there an AT&T repair site near you? Some bugs of this sort require special access to fix.