2000 Buick Lesabre Blower motor in-op

The blower motor in my Buick is acting up. It stop blowing at all speeds. When I checked the fuses (the fuse box is under the hood) there were no blown fuses but when I shut the hood the blower motor started to to work again. Then it stop working thet same day. I took the trim piece off to get to the blower and it started working again. There doesn't appear to be any lose wires and the connector looks good. I understand it could be the resistor but I'm not sure where to start without touble shooting the problem by spending money.
Any ideas???

Regards,