Use your meter on resistance measurement mode and measure across connector terminals on blower motor. Should be relatively low resistance. Let us know reading you get.
Look at terminal ends of motor connector. Does it look like they are both same distance back of connector face? If one or both pushed back, will not make good contact. Do they look intact and also not spread open more than normal? Check to make sure your wiring harness connector pins are also fully extended and in good shape.