We are trying to download this game from a disc purchased at Target. We have the box, but the only "Serial number" that we have is the one used as a scanner for Target. It would be the typical barcode.
If you bought the "Ultimate Edition" from Target (that's where I got mine about a year ago) then there should be a white label sticker, attached to the plastic case that holds the disk, that is inside the cardboard sleeve.
That sticker has the Serial number on it.
If it's missing, you probably need to return it to the store.