Be careful using a computer fan to vent fumes. Those things can't build up the pressure required to force efficient airflow around bends or through long hose. For that, you need a centrifugal fan. The kind one could salvage from a range top vent would be ideal. Smaller ones may do the trick, however, if the hood is fairly small. Radio shack where I am typically carries them.
What's important is to be able to feel a very gentle air flow just inside the opening of the cupboard. This inward air flow means fumes can't waft out. Definitely check the exhaust port to make sure you are getting a steady air flow before you use the hood for dangerous chemicals.
I also recommend sealing all the seams with silicone. Its an easy step that will greatly improve the suction and overall quality of the hood. Also, a light of some kind would be prudent.