Middle part of 3DSXL battery connector looks oxidized

A friend of mine has asked me to help fix their second hand 3DSXL, because it was only booting when the charger was connected. When I looked inside there was just coke everywhere. When I took a look at the battery it was oxidized on the negative and middle part of the battery. I tested the battery itself and it was was fine.

I tried putting my 2DS battery in (pushing it against the connector) and it still wouldn't boot. I've heard that the middle part is to prevent overheating. I then decided to take the 3DSXL apart further and I discovered that one of the middle connectors isn't reflecting like the rest. Here's an example of the 3DSXL connectors vs my NSMB2 2DS:

3DSXL (left of the middle)

2DS

Is there a way to remove the oxidization without making to much of a mess on the motherboard or could it be an entirely different issue?