You can try the method I used to use on my car, open up the tower and sit a mug or small bowl of vinegar in the bottom of the case, then close the tower again and leave it in there for a few days. This should disperse the smell, and the remaining faint vinegar smell should fade on it's own.
You can also use the follow up trick of repeating the process with coffee beans after the initial vinegar airing, replaces the vinegar smell with a nicer one that fades faster afterwards.
I'm not sure if putting liquid that evaporates into water and acid inside a PC case is very good for the components(!).
I did find at least 1 person doing it on youtube.. but it doesn't seem very mainstream...
I might suggest getting as much of the dust out as possible first to see if that reduces the smell. Besides which you want as much of the dust as possible out of the system first. But be sure to clean the PC safely.
Take the entire thing apart and give everything a good clean, removing all dust from fans and heatsinks. Sprinkle some bicarb in and on the case (when all thje components are still out) and leave it for a day.
Give it another good clean and put back together