I removed a little motor from my laptop fan and it won't run using a 9V battery
You are on the right track, in thought process at least, not procedure.
Know that fundamentally, there is no such thing as a DC motor. All motors operate based on changing (alternating/rotating) magnetic fields which are produced by changing (alternating) currents. They are all &quot;AC&quot; so to speak at the lowest level. What goes into the coils is always some form of AC.
You only have motors that take DC and convert it into AC. The brushes on a brushed motor do this by taking the DC you put into the wires and making the current change directions through the coils when it turns, thereby producing the &quot;AC&quot;, so that it can continue to turn instead of just turning a bit and locking up.
In a brushless motor, like your computer fan, electronics are required to do the job of the brushes. It needs some smarts. A computer fan has the electronics integrated into it, but it appears you might have ripped those out.