Referencing the attached diagram. The Pawl #347 and Toothed Element #353 engage and click when you pull the lever up, and release when you push the button. What is probably happening is that the Pawl is stuck in the released position and not catching on the teeth of the Element, probably because really old grease is is causing it to stick.
The fix is to disconnect the cable by screwing the adjuster all the way out, remove the lever, dismantle the Pawl and Toothed Element, and clean and re-grease them. NOTE: the pivot bolt is left hand thread, so it's Rigthy-Loosey, Lefty-Tighty!
There is a small chance that the teeth have worn off the Pawl or Element. This is what happened on my 230sl.
Good luck,
CT