Battery problems, bootloop, itunes error 4013

Hi all.

I just got a weird iphone.

The iphone wouldn't charge anymore, it was stuck on the charging screen.

So I replaced the battery, but now with the new battery I am stuck in a boot loop ( 3 sec on, 3 sec off). (And the problem with the old battery stayed the same.)

This is what I tried:

- Hard reset

- DFU mode

- New battery

- No front camera attached

- No charging dock attached

- No screen

- Those things combined

Now I got a little bit further, while in DFU mode itunes finds my iphone (only then) and I could press on "update". But while updating I got an itunes error 4013.

With the old battery I even can't get into DFU mode.

I don't know what is going on, can anybody help me?

My only solution I can think of is resetting the device, but I dont want to loose all the data on there..

Thanks in advance.

iPhone 6

iOS 6.2.?