Hi S., I have the same age children as you, my oldest who is now in kindergarten was just like this. She also would sit on the potty for a half hour or so and then three minutes into giving upwould wet her diaper. I understand how frustrated you are! The thing that worked for me was that I threw away the diapers, so I told her, she believed that there were no more diapers in the house, so she had to wear underwear, she hated to be wet or dirty so a couple of accidents and she figured it out that she had to go on the potty. You will have to be very vigilant, watch for clues as to when she has to go, or as i did fill her up of water and juice etc and after that put her on the potty, she will eventually start to go. While she is going cheer her and explain that she is going pee (or whatever you want to call it) and that you are proud of her. She may be scared and once she realizes exactly what "going pee" is and that it wont hurt, she will be more apt to do it again.
Hope this helps. Oh, also she is still young to get up at night to go potty so hide the diapers and after she is asleep in her bed at night, slip a diaper on her, before she wakes up in the morning slip it off her, she'll never know she had one on and hopefull it will begin to be dry in the morning, and even if it isn't get her into the habit of going straight to the potty first thing in the morning. Good luck!
Krissy