While coasting at very low speed with foot off accelerator or brake, into a crowded parking spot, the brakes failed after foot applied to the brake petal. This caused our vehicle to collide with a vehicle in front of us, pushing it a few feet backwards. Despite strong effort to push brake pedal down further, car would not stop. Pushed circular park button simultaneously with emergency brake tab which we believe ultimately stopped the car. No usual parking system alerts, beeps, lights, etc., turned on during the collision or near pre-collision. Finally, when car reversed to go home, the car made an unusual jerking movement without the usual reverse 'beeping' noise for the hybrid. Car then behaved normal for the 10 minute tense drive home. We are afraid to drive the car for fear of fatal brake failure to ourselves or others. Vehicle is intact and currently at local Kia dealer for past several days, though purportedly they 'found nothing' and are offering to return the car. Auto claim still pending and once car returned to us, we will have auto insurance rep evaluate the car.