What are the batteries underneath the battery for?

I'm talking about the two silver circular batteries that sit underneath the actual rechargeable battery. I included a photo.

I'm dealing with a controller that suffered water damage but would power on when it was plugged in. I wanted to open it up and see if I could just clean it out to get the battery charging but if not planned to replace the battery. Cleaned it up, put it back together and now it wouldn't turn on even when plugged in. Now that I replaced the battery and the battery contacts, it still does not power on. I did notice discoloration (burn marks?) on one of the circular batteries underneath. Short of the actual board being bad this is the only thing I could think of but I'm not sure exactly what their function are and if could cause this issue.