וַיֵּצֵא אֲלֵהֶם לוֹט הַפֶּתְחָה וְהַדֶּלֶת סָגַר אַחֲרָיו:
“And Lot went out at the door to them, and he shut the door behind him.” (Gen. 19:6, 9).
In a new apartment, a door between two rooms doesn’t open and will remain shut. Even if the door could be opened, the tenants are putting furniture on one side of the doorand will not be opening it. To me this sounds like a halakhic wall not a doorway. Would this require a mezuzah or not?
It is clear from your question that at one time the door was made to open, and it still has the door frame. If that is the case, some poskim rules that it still requires a mezuzahwhile others state that it does not.
Shulchan Arukh rules (YD 286:18) that even if a house has multiple doorways and only one is regularly used, all of the doorways must have a mezuzah. To this, Rema adds that if there is a wine cellar that has a large door for delivery of the wine barrels, that only the smaller door that is used all the time for going into and out of the house needs a mezuazah, not the large door. He does not explain why the larger door is exempt.
Shakh (YD 286:26) indicates that the difference between the two cases is whether the secondary door is always available to be used, even if people choose to only use it occasionally, in which case it would require a mezuzah, or whether the door was never used except under certain circumstances (when wine barrels were being delivered), in which case it would be exempt. According to this, certainly if the door is sealed or obstructed it would not need a mezuzah.
In contrast, Arukh HaShulchan (YD 286:40) rules that the only reason Rema’s case is exempt is because it is a delivery door and not a door for normal entry. According to this, no matter how rarely someone uses a door, it is obligated in mezuzah if it is a normal door for entry and exit.
Arukh HaShulchan goes further and writes (268:38) that “since any doorway that one has in the house is obligated to have a mezuzah, even if people do not use it regularly, then no act of trying to negate its status as a doorway would be effective, short of destroying the actual doorframe… Even if a person but a large cabinet in front of it to make it impossible to go through the doorway, nevertheless, it remains obligated in a mezuzah.”
Given Arukh HaShulchan‘s strongly stated position, although it does seem like a heightened form of formalism, and is seemingly not the position of Shakh, I think a person should be strict and put up a mezuzah without a berakhah. It does not have to be the most mehudar mezuzah in the world.