The Realtek is the direct replacement card for your laptop. I would recommend sticking with it because there may be some compatibility issues with other brand chipsets like Intel but technically any minipci card will do (not the minipci express).
It might need a new jack socket. Just be sure to test your power supply for the correct voltage but if your laptop powered on with the battery, I think the culprit is the connection.
That battery is the CMOS battery