In your case, since you decided to put the door out of use permanently as you moved in, it is exempt.[1] If the door was only being blocked temporarily, it would require a mezuzah from the outset.[2]
If the door was originally in active use, but now you have decided to block it permanently, many authorities caution against removing its mezuzah, even though it would then seem to be superfluous.[3]
[1] Shevet HaLevi Y.D. 92, cited in Pitchei She’arim 286:205. Agur B’ohalecha (24:15:32), citing Sefer Eshkol (24), contends that even if one decides mentally to put the door out of use without demonstrating this intention through a physical act, it is exempt.
[2] Agur B’ohalecha 24:15:32.
[3] Teshuvos V’Hanhagos 2:540, citing Aruch HaShulchan 286:38; Shevet Sofer 92. Also, if later you would decide to unblock this door, you would not need to remove the mezuzah and affix it anew. Pitchei She’arim (286:205), citing Mezuzas Melachim (10), explains that since the mezuzah was originally placed correctly, it does not lose its status. Thus, the requirement “to affix a mezuzah and not to use one that is already affixed” is fulfilled. See Kitzur 11:13.