its cooler wouldn't spin.
I replaced it with a new cooler
There's a terminology issue here.
What exactly did you replace? Note "cooler" typically suggest a heatsink with an attached fan - often referred to as a "heatsink fan assembly" or "HSF".
To say the "cooler" wouldn't "spin" suggests the cooler's "fan" had failed and would no longer spin.
So when you say you replace it with a new cooler, what do you mean? Did you replace just the fan? Or did you replace the entire heatsink fan assembly?
If just the fan, is it an identical replacement with a fan that is rated to move the same (or more) amount of air (CFM - cubic feet per minute) at the same RPM (revolutions per minute)?
If the entire HSF assembly, is it an identical replacement or something better?
And if you removed the entire HSF assembly, did you properly clean the mating surfaces and properly apply a fresh, new layer of TIM (thermal interface material)? Old TIM must never be reused.
Note, if you only replaced the fan and not the heatsink too, "IF" you broke the cured bond of the old TIM between the heatsink and processor, you still need to pull the entire assembly, thoroughly clean away the old TIM, and properly apply a fresh new layer. Not doing this will result in inadequate transfer of heat.