iPhone 4 boot trouble

I have this strange problem where my Iphone will not boot at all when it is disconnected, I don't even get a low battery problem. When I connect it, after a few seconds(10-15) it will start to boot but then suddenly it shuts off, and its another 20 secs for it to do the same. If I disconnect it while it boots, it just shuts down. I managed to get it into DFU or the other mode and tried to restore but when iTunes restarts the phone its like it loses control over it and the phone goes into the boot loop. One time I got a error 21, the other a 1600, but that was when I was trying some more extreme things(stitched 5.1.1 downgrade)

I suspect it may be the battery but I really cant tell.

Its an iPhone 4, 16GBs GSM model iOS 6.1

Thanks!