iPhone 4S restarts randomnly

Okay the iPhone 4S is on iOS 6.1.3 and it restarts randomnly

I took the liberty to open it but could n't diagnose the issue ... Logic board is fine as well as the battery

What i've found is the phone goes well when it is plugged in for charging ... The problem arises when the phone is left unplugged but it is really severe since the battery goes to 0 % in a couple of hours and you can do nothing

Someone diagnosed it might be a cable connector issue but i am unfamiliar with that

The problem is not software related as I have already made several attempts restoring in recovery mode with new setup, backup restore and DFU restore as well.

Also, When the phone reboots randomnly, it shows something for a second and then reboots ... the text is here

[NAND] _Findflashmediaandkeepout:600 physical nand block offset 1

[NAND] Start:355 this 0*8600a300 provider=0*86014580 flashmedia=0*86014580

[NAND] Wmr_start:149 apple PPN NAND driver , read/write

[NAND] Wmr_start:174 FIL_Init [ok]

Anyone could help me further with or anything else will be highly appreciated ... Thanks:)