Cleaning a Ventilation System?

I'm about to move to a new apartment, and now I have clean up my old apartment before I give it back to the landlord. I have to clean this "air ventilation system" which I never use. Anyway, I opened it today, and it's dusty as hell. Canned air, compressed air isn't going to do the job. It's just a huge metal thing loaded with dust inside.

The worst part is the outside layer of the ventilation system is all full of dust. I don't know who designed the system, but the outside frame which allow air to go in is filled with tiny little boxes (which are very dusty). I have to put tissue on my finger and clean the tiny little boxes one at a time. It takes forever. I was hoping if there are some tips.
Thank you very much.

jimbo0427 from CA