On my 2004 Automatic Sonata the button on the gear shifter didnt work. I removed the knob and the plastic rod that is pushed down by the button on the knob was broken off at the top. I can push it down by hand and change gears. What part do I ask for to replace it?
Most parts counter staff are pretty good at figuring out what people want, your description in your post is great, go with that and the parts in your hand to your dealer and let them serve you brother!