If your PSU fan isnt running, and you have at least a moderate level PSU, it will have overtemp protection which will shut down your unit automatically when it over heats and it will with no fan running. It only pulls temps from a few points in the power supply which means you will have hotter spots which may cause the PSU to go out of spec without its protections kicking in which can be damaging for components. I would not continue trying to run the system until you replace the PSU.
Ok I bought the new power supply, I installed it perfectly fine, Turned on the computer and it says my system was unable to start. what the hell happened?