I don't think I'd say BIG chance. But I would certainly say A chance.
Might want to take a look at all the metal contacts on the side that faces the motherboard, and make sure none of them are screwed up or damaged too. Probably might need a magnifying glass or really good reading glasses to see it up close and get a good look. Also might want to look at the pins on the motherboard the same, and make sure none of those are bent or damaged.
Also, the CPU fan cable is only supposed to attach to the fan header in one way. Make sure you have it on there with the notch in the cable located in the same position as the cutout on the fan header. It CAN accidentally get put on backwards, but you have to almost TRY hard to do that because it won't want to easily go on wrong. But I've seen it done plenty of times.
Also, make sure that it IS the CPU_FAN header, marked just like that on the motherboard, that you are connecting the CPU cooler fan to. There may be other fan headers in the same area but it must be the CPU_FAN header you connect it to or it won't work.
Does the CPU fan come on when you power up the computer? If not, then something is clearly wrong because that should happen no matter what else is wrong.