Translation:I do not turn on the light in this room.
It's debatable. The difference between the "Saxon genitive" (X'-s Y) and the "Norman genitive" (Y of X) is that the possessor (X in these examples) is animate in the Saxon genitive and inanimate in the Norman genitive. Generally, people will only say "the roof of your house" and "Michael's sister" instead of "your house's roof" and "the sister of Michael". However, most native speakers aren't consciously aware of this rule - It's one of those "things we don't know we know", and if you did say "your house's roof" or "the sister of Michael", it would be obvious to everyone what you meant, even if you might get some odd stares. I would say what you wrote should have been accepted.
The Japanese imperative form is different from a regular verb form. Per my reply to another comment:
If you leave out the subject in English, it becomes a command. The Japanese sentence is not a command; the subject is merely implied, so it could be "I"/"you"/"he"/"she"/"they"/"we".
I put the answer "This room's lights do not turn on," and I understand that I got it wrong because of a transitive/intransitive difference in the verb. How would you write this incorrect sentence in Japanese? Still trying to understand this transitive/intransitive verb thing.
つける is the transitive verb "to turn on/to light"- You do the action of turning on something else. It takes the wo particle when the action is or will be taking place, or the topic marker when you're not currently doing the action but used to show contrast (this light I don't turn on but others I do) . 電気をつけません - I do not turn on the light, or 電気はつけません - (As for) the light, I do not turn it on.
The intransitive つく "to be lit/to be turned on" would be used for something that does not do the action of turning on. 電気はつきません - The light does not turn on.