Hello!
DO I understand this correctly that 1) your iPod works fine through the dock connector on the bottom, and 2) you cannot locate the connection on the logic board to plug the headphone jack cable into it?
If so, it sounds like an all-too-common problem with the iPod Mini: the headphone connector pulled off of the logic board. If you look at the headphone jack cable, is there a piece of plastic stuck on the connector?
If you look at [product|196002|this picture], the headphone connector is the black rectangle on the edge of the top left of the board.
If this connector is missing, you unfortunately need a new logic board.
Sorry!