Yes the fan should turn on. Seems weird that the corsair fried itself so quickly, but it is an electronic part so stranger things have happened. If it worked for 3 days and then the PSU fan won't turn on when you try to start the PC, then you have another faulty PSU which you would need to re-replace it. For the system you have, a quality 450 watt would do just fine. Another corsair, antec, seasonic, thermaltake... Those are the brands I'd stick with, not necessarily in that order.
Note: This is all assuming all cables are fully seated in their respective connectors.