Hardware issue or what?

Hello, I have problem,
I own two iPhone 4S:
1- Battery's dead, I tried with a functioning charging circute but nothing! Instead it has a working logic board.[/B][/I].
2- Logic Board's gone but everything else still works!.

So I decided to create a new iPhone with the two I have.
Obviously panels, frame and components from terminal 2 and logic board from terminal 1.
First check ok, iPhone Frankenstein 4S go through boot and the system started properly. I needed to initialize it to give it to my gf, once I did this from the iPhone here I had "Hello, Hi, Ciao" etc.., but when I inserted the wifi PSW to set the phone, it just couldn't go through it giving an error.
I decided to go DFU and work from my MB. Here come the troubles.
iTunes try to initialize the iPhone, but at 70% appears 2001 error.
From that moment the iPhone is on boot loop, and if I try to DFU and initialize from iTunes it returns 3014 or 2001 error.

Is it possible that batteries, althought they come from same devices are different?
Infact APN codes are:
Device 1 (dead one but sister with working logic board) = APN 616-0582
Device 2 (working one) = APN 616-0580.
One more thing: the iPhone works only under usb current, if I take it off the iPhone just turns off instantly.

Will a new battery with the same APN number with the dead battery (which I say again, was the one sister with the working logic board) solve my problem??
Thx