ST56F 

No.

A hard disk only consumes around 3W ~ 10W+- at most. Adding one extra hard disk doesn't mean you need to get a better power supply. Many people make the mistake of getting a high capacity power supply just because they have e.g 3 ~ 5 hard disks.

There are some reports that the ST56F has a stop-start type fan, where the fan stops when the load is low and starts when the load starts increasing to a level which can generate quite a bit of heat. But such information is not confirmed, and neither does Silverstone state such a feature.

Anyway, these are the possible reasons for a fan's failure :

1) Worn out bearing
2) Worn out motor
3) Clogged up by dust

If your power supply is still under warranty, and the fan has not acted in such a way before, then proceed to RMA it.

Try stressing your GPU too while Folding@Home by using MSI Kombustor. That should create a load enough to instruct the fan to keep on running to cool the power supply.

If your fan is indeed problematic, you can consider replacing the power supply's fan yourself by getting yourself a good 120MM fan e.g the Arctic Cooling F12 120MM Fan or the Cooler Master Xtra Flo 120MM fan ( if you do not mind a high-speed fan with a loud noise ), and also by getting yourself a 3 pin to 2 pin converter via this seller. Since your power supply is out of warranty, it probably wouldn't hurt to open up your power supply . But be cautious when opening up the power supply. You do not want to brush against the capacitors or anything else otherwise you could get shocked.

Edit : His is a 2 pin to 3 pin converter, not the other way round . You may want to hunt for the converter from another place, or attempt to mode wires .