I've spent some time on this and have learned a lot...In your case, the little tabs on the other side (the working end) of the Push button(s) are probably broken. I took mine apart a few days ago and discovered this condition. You would be amazed as to how intricate and flimsy the assembly is. So with a little ingenuity and some glue, I managed to get them working again. However, the EC light remained on so my problem runs deeper than that...
I took it to my mechanic who informed me that yes...a constant EC light means the system is low on refrigerant (1996 S class on up)...and sure enough, he had to charge the system and add a dye pack to find the leak. It will take a few weeks to bleed enough to trace.
My climate controller, however, seems to be missing some brain cells...it still thinks the system needs refrigerant even though it has been charged...the light sporatically comes on. It too probably needs to be replaced.
MB wants $866.70 for a new one...pretty stiff, my mechanic says he can get a rebuit one for approx $500.00 and in the meantime, I'm looking for a used one. Not much luck at this time.