Just as background, since it does sound like parts of your systems are not functioning properly, on the W201, the center vents are for "NON HEATED" air only, which means that outside ambient air and chilled a/c comes from the center, but not any heated air, which is directed from the side vents and up/under the dash. A lot of owners without the original manual don't realize this "design" feature.

The climate control/fan speed unit can be removed without taking out the whole dash pad. You will need to remove the radio, ashtray, etc. The unit is held in place by pressure clips on the edges of the unit. When I removed mine, I just took out the entire center console.