It depends on your cooler fan. If it's RGB or ARGB, then most normally it'll have 2 wires. One will plug into the RGB socket, it's kinda big 4 pin that resembles molex. The other will be a somewhat small 3 or 4pin that plugs into the cpu_fan header. Both are required for operation as the small plug is just for the fan, the bigger plug just for the lighting.
If you have a cheaper/older style LED fan cooler, it'll have just the one small 3 or 4pin plug that goes to the cpu_fan header. IF that is what is done and correct, and the lights are on, but no fan spins, first check the bios and temporarily set the minimum speed for 100%.
If that doesn't work, the fan is no good and should be returned/swapped