Can this boot loop problem be fixed somehow (Galaxy S3 mini)?

[AC Question]

I got my phone (Samsung Galaxy S3 mini) from a cousin and from the day one, he had one problem - when it is connected to charger, as soon as battery goes over 93% phone restarts itself in an endless loop (until I disconnect it from a charger).
Phone was working very well for a year like that, and couple days ago in a middle of a conversation it restarted itself and now it is in an endless loop. Phone boots up, there is Samsung logo, there are my icons loaded, that lasts for three seconds, and phone reboots. This repeats until I pull the battery out. If I press power button again, this repeats.
To sum it up: my system boots up, works for three seconds and reboot.

More info:
-Phone was never rooted, there are no custom roms on it, it is updated to latest version available for this phone (update was done year ago).
-Cleaning cache partition didn't help.
-Booting in safe mode didn't help.

Can this problem be fixed (I guess it is hardware problem), without loosing my files that are in the phone? It is very important to me to get access to these files since phone basicaly doesn't support moving anything to SD card (besides music and camera photos)...

Is there repair for this? I'm guessing there's a problem with chip on logic board...

 

[belodion]

Does it work if the battery is only partially charged?

 

[Rukbat]

It sounds as if it's throwing a dendrite at 93%. That reduces the voltage at the battery to 0, making the phone reboot. You need a new battery.

(To read about dendrites, see Lithium Battery Dendrite links. You're not the only one with the problem. A little thing called "the entire automotive industry" has the same problem, and is spending billions in an effort to find a way around it.)

 

[dusan92kov]

belodion, now it happens at any battery level.

Rukbat, I bough new battery yesterday, same problem.

 

[anon(632115)]

When in a loop, remove the battery and wait a few seconds then replace it. Does it turn on if you don't press the power button?

 

[dusan92kov]

Pugs1957, I said it above, no, it will only loop If I try to power on the phone; if I pull the battery out, phone won't try to turn on. I mention that so that faulty or stuck power button can be ruled out.

 

[dusan92kov]

Ok, I have really weird update on the situation...
I was experimenting all the time, trying to make this work somehow, and what I tried was to plug in USB cable (connected to my PC) into the phone, the moment it boots up... Couple of times phone remained on for longer period (even up to 15 seconds, and that never happened before)...
Could the faulty USB port causing all of this?