Ok, these are the exact problems I have.

1. The door locks will not work at all
2. The Headrest button will NOT work at all
3. The Trunk AJAR button will NOT work

But, whenever I press any of those buttons, I hear the PSE pump working

However,

The door and trunk suction both work.

Also, if I lock the car(the door) and I unlock, it will NOT re-open. Sometimes I need to disconnect the battery, sometimes fuses.

Any ideas??

There are two pumps in the car, one to draw in the doors and trunk lid, it resides in the trunk above the rear wheel. The other is under the pasenger rear seat, it provides pressure and vacuum depending on the direction it is running, The doors, gas lid and trunk lock are provided pressure to unlock vaccum to lock. The pump provides pressure for the lumbars via a eservoir, and supplemental vacuum for the HVAC thru another reservoir when the engine is not producing any. The back up rods (if you got them) trunk handle and headrest release ( if you dont have electric) are also served. The pump has safeties for pressure, time depending on the circuit, 10 seconds in lock circuit 60 seconds for lumbars and HVAC.
Be carefull pulling off hoses, if you break a nipple you are screwed. In the mid 90s there were some defective pumps with a bad internal hose, MB had some so you could replace them, I doubt any counter guys will recall. There are really no replacement parts, altho rebuilts are available.
There are also two styles one with a plenum that terminates the hoses the other is made up out of "t"s and splitters and caps

Where are such rebuilds available, please, for my 95 S-320 LWB?

idk if this helps. i need a pse pump. my doors, gas tank and trunk dont work electrically. my head rest button does work tho. you can find a used pse pump online for about 130 bucks but i have seen like 4 different pumps supposedly for the w140s

o yea the soft close works too

Part numbers must be exact although, there are some that are interchangable...google it and research it