Does your owners manual shed any light on A/C airflow?

Air distribution is controlled by a complicated system of vacuum valves and actuators. I would look first for a large vacuum leak such as a hose displaced or rotted out. If DIY, and all easily seen underhood hose connections are secure, it will then require removing the underdash panel and some gymnastics to inspect the hases and valves in the dash area. A pro would use a smoke generator to zero in on the problrem. Good luck and please let us know the resolution.

In some older M-B models the center vents provide hot air only and no A/C air comes out of them.