95 Grand Am intermittent blower motor

My 3.1L Grand Am has been having a problem where the blower motor sometimes isn't working, on any speed, when I start the car. Eventually it'll all of a sudden kick on and stay working until I shut the car off. When it is working I have all speeds and hear no abnormal noises coming from the blower motor. Would this be a sign of a sick blower motor or just the resister pack? On a possibly unrelated issue, I've noticed that the plastic housing around the blower motor under the hood seems to have rotted away and the pieces simply crumble in your fingers. Not sure if this is due to age, some chemical reaction, or possibly heat from the blower motor?

probly should start by checking the wiring/ciruits .
And a visual inspection of the blower motor,
could just be a loose connection or the motor has gotten wet.

On the crumbling,
is it a foam seal thats rotting or the cover its self?

Wet motor could be at least part of it. The cover I'm talking about is the hard plastic shell over the blower motor. At least its supposed to be hard plastic.