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This recently started happening. I replaced the relay thinking that was it well... Nope. If I have the ac blower on and pop the hood and give the motor a tap it starts. If I let it sit over night have to go through same process. I thought it was resistor but from what I read that would mean only would work high or low it works in everything once I tap the motor.
Most likely you've got a problem with the motor itself; the tapping remakes a lost connection.
You could use a meter and look for power at the resistor connector when the motor won't turn, go through all speeds to make sure the dash switch is working too. If power is available at all terminals in sequence then I'm right back guessing its the motor.
Good news is they're not horribly expensive or difficult to change.