Well, it it is -->THIS
<-- , then it is not a good power supply to be honest. Has less power then a quality 250 watt unit.
If it was a newer seasonic based unit, I would guess it is a feature as those do not run the fan under 20-30% load.
Only thing I can say is to run the system for a bit and see if it starts. The fan may be too hard to turn and the power supply starts at full speed then drops it to a point that it can no longer turn it.
Your option then is a fan swap OR new power supply.
Just do not load up too much on that power supply.