I turned on my Heil furnace for the first time this fall, only to find it didn't work. After looking at the furnace, I heard a slight hum, like the motor was trying to engage, but the fan wasn't spinning. I turned the power off and check to see if the fan was jammed somehow, but it spun freely.

Is there another possible problem, or do I need a new motor for the fan?

It is possible that the induction fan is defective but before replacing it I suggest you check for the proper voltage to the fan when it is supposed to be running. Inside the blower door is a diagram and if you have a electric meter and know how to use it you can check it out yourself if not call for ON SITE service. Many times it is cheaper to call for service than it is to play the EXPENSIVE parts replacing game.