I have built a system for my sister and I'm having this problem. The power supply fan starts to spin for a second, then stops. I have triple checked all connections, and even went down to only cpu, mobo and psu. Still nothing but a slight spin.
it can be a faulty psu. i had a power supply do the same thing to me and i would push the fan with a finger to jump start it...later on the fan would start up automatically but the psu broke 4 months down the road so if its working weird now replace it while you can
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.