A lot can happen in four months, such as excessive wear on the brake pads due to stuck calipers, a leak in the hydraulic system, etc. This reminds me of the people who say, in regard to any automotive problem, “How could this happen? I had the oil changed a few months ago.” That is sort of like the person who believes that he should not have had a heart attack after visiting his dentist/podiatrist/orthopedist/chiropractor. In other words, one situation is almost always not related to the other situation.
Did you have any unusual noises emanating from the car in the week prior to the incident? Was your braking action “normal” up to the time of the incident?
The “emergency brake” actually engaged as soon as you applied it. But, since it applies braking power only to the rear wheels, it has limited ability to stop the car, thus the feeling that it only engaged 100 ft. from the toll plaza.
You have to be A LOT more specific on the reason for brake failure in order for us to give an opinion as to whether the dealership might be at fault. What does the repair invoice state?