Battery does not charge, without battery 10sec holding power but works

Hello Guys!

So here is my story:

I live in Brazil and there's no kind of repair shop that could help me and I'm trying to solve my problem about 2 years already, without having to buy a new logic board 820-2850-A, for my A1286 Macbook 15", i7. The board here costs about US$800... a new macbook, well... I don't even want to talk about it hehe. The authorized repair shops technicians are kind of lost too.

The cause of the problem was not-original charger (I know, I'll never do this again) that blew up and the consequence is that the battery does not charge anymore. It runs with the battery charged, but magsafe does not charge the battery. I've already tried a new battery and even replaced the magsafe conector board (820-2565-A), but no success at all. I've been using the laptop without any battery and holding before and after 10 secs magsafe is plugged in for almost 2 years...

I wish you could help me at least guiding what I should do, because even with schematics of the logic board, I don't know how to recognize each component. But what I already did is to find burnt components. And I did it! I could send you pictures of the resistor that is burnt, that is very close to the battery connection to the logic board, so I assumed it could have something to do with it.

Here are the pics with the resistor

https://drive.google.com/file/d/0B1Ku7ym...

https://drive.google.com/file/d/0B1Ku7ym...

https://drive.google.com/file/d/0B1Ku7ym...

Does anybody know what this resistor stands for?

Thank you very much!