I need to know which of these sentences is right ?
My room light doesn't work.
My room's light doesn't work.
The second sentence is definitely correct.
The first sentence is also correct. In that sentence, room is a noun modifier applied to light:
We often use two nouns together to show that one thing is a part of something else:
the village church; the car door; the kitchen window; the chair leg; my coat pocket;
Much like the kitchen window means the window that is part of the kitchen, the phrase my room light can mean my light that is part of my room.