I wonder where we can make genitive without 's or of. I know that using "of" in "dorm room door" might be complicated but the question is when we are allowed to make such phrases.
Swan in Practical English Usage has an entry called noun + noun: advanced points. In the parts section (p360) he states:
We use the 's structure to talk about parts of people's and animals' bodies.
- a man's leg -- an elephant's trunk -- a sheep's heart.
But to talk about parts of non-living things, we usually use the noun + noun structure.
a table leg (NOT
a table's leg)
a car door (NOT USUALLY
a car's door)
This is not a hard-and-fast rule, as indicated by the not usually in the last example. Nevertheless, it is a useful guideline for English language learners.