Limited brake after starting

My 2004 Prius has limited braking power after starting until I pump the brakes once. For example, if I clime in, put my foot on the brake, start the car, and put it in gear without taking my foot off the brake the car will tend to move against my will. If I press the brake very hard I can keep it from moving. Or if I release the brake once the braking power will return to normal. I have no other braking issues. And if I release the brake after starting the car and before putting it into gear my brakes will be normal. I took it to the dealer and they were unable to figure it out.

Does anyone have any suggestions?
Thanks for your help!

 

No trouble codes that Toyota told me about but they may just not have told me. Brake pump noise sounds about the same but I can't say I pay enough attention to know what it sounded like before this happened. It's been like this for quite a while without any change.

Again, no codes that Toyota told me about and one would assume that the other items on the list were part of their diagnosis. I'll bring it to my primary mechanic (not Toyota) and have him take a look and check for codes. And I'll ask Toyota before that if they noted any codes. Presumably, they would write such things down in my service record.