I have a Goodman A32-05 Heat Pump and the blower fan will not start unless I spin it, and then it runs fine. What could be the problem?

It sounds like you need a new capacitor for your motor, eithet that or the bearings in your motor are so tight that is will now start on it own

First which motor is it that will not start? Is it the furnace blower motor or a Heat pump outside unit.

If it is the furnace motor you will need to find out the size capicator you will need, probably the easiest way to do this is to turn off the current to your furnace, and find where the capicator is, most of the time it is attached to the front of the blower housing. It should have two wires connected to it and these should be covered wiwth a rubber guard. Disconnect the wires, lossen the screw holding it in place and take it to a dealer for motors and he can tell you what size it is and should be able to sell you a replacement.

Re-assemble and re-connect the wires. It does not matter which wire goes where but be sure they are on on the sane post coming out of the capacitor. You will see that each post has two or four places to attach a wire.