Intermittent Air Conditioner Issue

Hi, I was hoping someone could help diagonse this problem. When I start my car, a/c blower sometimes doesn't start. I'll have to open the glove box and slam it shut and then the fan starts blowing. I've opened up the area where the in-cabin filter should be and if I nudge the rotating thing, then it will start moving. Is this a case of it just being dirty?

Thanks for the help in advance!