By hardstuck, do you mean that is wired directly to the motherboard? If so might want to share a picture of the issue to help us paint a better picture. If not hardwired, a CPU cooler fan should be connected off a fan header on the board. If you wiggle the fan connector from left to right while maintaining an upward pulling force, the connector should be free.
Again, please pass on a picture so we're both on the same page.