Problem with dock connector (Possible short circuit)

hi, my name is julio and i need help with my iPhone 4.

So my iPhone keeps in loop apple logo but just if it connected to a computer or a ac power adaptor. If i remove the cable the iPhone goes down. I try replacement of battery but nothing helps. I think the problem is with dock battery connector because i search a little and i found this image:

IMAGE

So i pick up the multimeter and i check the continuity. I note that The last pin and the first pin are on short circuit. I think that the first pin is ground ant the last is vs (red wire) so make sense the power problems but i don't know how to fix this short circuit.

I'm asking for help to solve this guys.

Thanks a lot.