It seems you got a few things mixed up. Allow me to show you how I parse it.
・なければおかしい is a clause modifying 部屋
[なければおかしい]部屋 ⇒ a room [that it would be strange if it didn't exist]
・本来なければ is not the negative version of 本来ならば (It never is!)
本来 here is an adverb that modifies (or is part of?) the relative clause.
[本来なければおかしい]部屋 ⇒ a room [that, normally, it would be strange if it didn't exist]
So, 本来なければおかしい部屋 is a noun phrase, acting as the subject of the clause 本来なければおかしい部屋 + が + ない (a room doesn't exist that, normally, it would be strange if it didn't exist).
Lastly, 本来なければおかしい部屋がない事を指摘する I'd translate as:
(...) points out the fact that a room is missing that naturally has to be there.
or something along those lines.