to fix the fan your going to have to open the power supply up, the first ting you must do before you open it is unplig the computer and puch the powerbutton on the computer once, this will drain any eletricity out of the power supply. once you open it make sure that there is nothing cought in the fan like a glob of dust. if there is nothing blocking it then take the fan out and splice the ends of the wires. your eather going to need another computer or 12v battery. if you have a laptop battery that will work. but another computer will do it the best, you are going to have to plug the red splice from the fan wire into the yellow wire of a pc connector, and the black into the black part of the connector. like te picture below. if none of these steps don't work or you just don't want to do them, then you could just go buy a new fan, or get a new powersupply.

most powersupplys don't have the temp regulated, because the tempture can rise very quickly in a powersupply, and the cooler it is the more watts it will make. the fan might not be dead, one of the solder points could have just seperated.

I have a similar problem with mine... But what I do is when it doesn't start up at boot, I just use a pencil to boost the fan for a jump spin then it goes by itself. It stays on for the rest of the time as long as my computer is on and its pretty old so it doesn't have a temp thingy.

Yea there's basically nothing wrong with it.. just needs a jump start most of the time and it runs continuessly until i turn off the PC