Looks like a backplane ( motherboard ) would be needed. MPU board maybe too. Can't tell from the picture which connector it was that burnt, could guess, but a picture of the entire board would be better.
The manual information is on the site in the download section - you would need to be a contributing member to download, probably cheaper than trying to purchase a manual from sites online. Plus lots more info on everything in the machine in the download section too.
The vendors on the home page can get you any parts you may need. You will see they are here helping everyone if you get the time to check out any of the posts. Check the classified ads for parts too. To list there you need to be a contributing member, another plus.
Once you determine the connector and pins that fried - you can try to determine what might have taken the board out. With the battery leakage - that is most likely the main cause.
May be able to repair the damage on the MOBO and even the MPU board. Some members do the repairs, search a bit and you can see what is on here.
Good luck with your new machine, many here to help. And welcome.
Tony