This could be several things really. Off the top of my head:
1) Fan's not plugged in or not plugged in properly. I have on occasion "missed" plugging in the fan connector to the three-pin connection on the motherboard and was off by one pin. (That is, only two of the three pins are connected to anything. One was just hanging out in the air as it were.)
2) Fan's plugged into a motherboard with fan management turned on. The motherboard would only turn on the fan when the motherboard exceeds a set temperature. When it does turn on the fan(s), it uses the lowest speed possible to reduce the temperature to the range it's targeting. It does this to reduce the noise level and power requirements.
3) Fan's plugged into the "FAN-ONLY" molex connectors of a power supply with fan management. The power supply would only turn on the fan when the power supply exceeds a set temperature. Similar to #2 above, but using molex connectors to the power supply rather than the three-pin connector on the motherboard.
4) The fan has failed. Of all the parts in all the PCs I've built over the years, fans are by far the component that fails most often. Case fans, CPU heatsink fans, video card fans .. you name the fan, and I've had at least one fail. Most of the time, they are cheap and easy to replace as your case fan probably would be. Video card fans are the most troublesome as they are often one-of-a-kind fans that are difficult to get replacements for. If the fan's dead, I suggest trying CoolerGuys
for a replacement.