98 Malibu: Blower motor electrical connection

The blower motor on my 99 Malibu either stops working or slows down randomly. The problem is at the female connector on the motor, where the wiring from the resistor plugs into. (Trust me, the resistor is OK). When I apply pressure to this connector, by pushing it to one side, the motor speeds up and runs perfectly. Could it be a broken wire? How can I remove the motor, to get a good look at the connection? I can access 2 of the 3 bolts holding the motor up in place. Thanks for any advice on the 3rd bolt which is tucked up above a round cylinder shaped thing in front of the motor.