Odd air conditioning problem

Recently I have had a problem with the air conditioner in my 08 Prius. When I first drive the car, all is well. When I stop somewhere, then come back to the car, the air conditioner will not come on. It will still show on my display that it is on and I can pick different settings, even though the different settings do not make anything happen. Sometimes I can turn the car off and on again a couple times and the AC will kick on. Today I just decided to drive with the windows down, and after 10-15 mins, the AC kicked back on.

It is still running cold when it is working, so that has not been an issue. So far it has always worked with the first start of the car and has not stopped working once it is working. Please let me know what you all think might be the problem and here's hoping it doesn't cost a fortune. Thank you!

 

No air at all but when it does finally kick on, it is cold air.

 

Thanks, I will check that out and see if the same is true for my car.