This is a fine noir tale with style. It has the straight-forward prose associated with the genre. If there's one aspect of the story that I think could be improved is using more variation in the paragraph structure, particularly the initial sentence. This is a great example that you used:

When Nancy woke up, the first thing she noticed was the rope around her wrists.

I like the structure of this initial sentence because it doesn't start with the name of the character. The sentence could have been written as "Nancy woke up, and the first thing she noticed..." This is fine too, but if too many paragraphs start like that then it becomes too repetitive. At least that's how it sounds to my ear, other readers might have a different experience.

The two could barely see, but they turned to each other. Nancy ran to the door and tried to open it, but it wouldn’t budge. They were locked in.

This is another good example of a great initial sentence that then carries the action of the protagonist further into the paragraph.

There is something to be said about the uniqueness of the noir style, which can be somber and melancholic. You did a superb job of capturing that aspect of it.