The usual culprit for that is a broken nylon plastic pushrod that is located inside the vertical section of the shifter. The handle on top has a cam inside that is pushed over by the button which pushes the rod down so the shifter can be moved out of Park.
The handle pulls straight up and off the lever. It is on there tight but no screws hold it, you just have to really apply some pressure to pull the handle straight up & off. You'll see the plastic (nylon) push rod once you get the handle off.