the PC beeps cause the cpu if overheating, the beep is the alarm for cpu-fan warning. if u use 4 pit fan, it is pwm controlled, it spins at different speeds, depending of the cpu load. but most fans have a limit to how low the voltage (rpm) can go. if below this point, the fan will simply stop spinning. try to set the fan to higher speed, maybe even full speed.
if this doesnt work, its probably a faulty fan, just replace it.