The battery is also attached to the circuit board by a cable. The cable is difficult to disconnect with both components in place. It's best to lift the circuit board out partially to give yourself more room to disconnect the connector.
The wire that is connected to the circuit board is connected by a plastic piece with two metal prongs.
Use the pointy end of the spudger to place in between the computer board and the plastic piece and gently pry the prongs away from the circuit board.