No air coming out of vents

Abridged version: My fans won't blow any air out of the vents. If I spin the blower/fan motor that is behind the glove compartment, it'll work again. But the cycle repeats itself every time I turn the car on.


I've searched around for answers for this, but haven't come across anything conclusive.
Here's the problem: air no longer blows out of my (2006 Prius) vents. First it happened one morning but was fine that afternoon, now it is an evey-time-I-turn-the-car-on thing.
What I've tried/noticed:
-when I turn the air on (temperature doesn't matter, neither does using the display vs steering wheel controls), I can hear a motor running under the hood (starts with a slight whir and steadily progresses, but again, nothing comes out of the vents in the car).
-I took out the glove compartment, removed the filter, cleaned it off, gave the fan motor a little spin (all with the car off). I turn the car on, the fans work.
-Next time I turn the car on, they don't. I repeat the last step (remove filter, spin motor). Works again. Every time.

The problem is, that's pretty annoying to have to do that every time I get in the car. Since everything "can" work fine, what do you think the problem is?
*I've scheduled a service appt with the dealership, but I'd like to keep it as low cost as possible (whether that's cancel the appt, or let them tell me what's wrong and do it myself if possible).