automatic transmission troubleshooting

[dua40]

Dear Sir,
I had a Maruti (Suzuki)800 TRD model (1992),a special car for persons handicapped with a limited functioning of the right lower limb.It is an automatic transmission car with an extra accelerator pedal to the left of the brake pedal.
The car was running smoothly for about 5 months when after its third free service it was found to have developed a snag. In the initial moments of driving in the forward gear, it took a slight jerk followed by a smooth movement in the same direction with a slight increase in the speed.
After some time,i.e. about 2 months, of driving the car with an alleged minor 'missing' defect in the car, one day while moving in the reverse direction after parking the car for some time,it just sped backward without responding to the applied brakes and crashed with a scooter parked behind. When the brakes did not work and the car kept on pushing the collided scooter, I thought that shifting the gear in the forward direction 'F', without applying pressure on the accelerator pedal,the car would stop automatically. I did the same, but to my surprise, the car sped in the forward direction, when I had to manage the high speed while any pressure on the brake pedals would not work (the accelerator pedal was left untouched).
Application of the hand brakes, also, had no effect. I shifted the gear from forward to the 'N' gear which did not help and then,I even shifted the gear to the 'P' gear which I knew was supposed to be applied only in the parking situation,but to stop the misbehaving vehicle I had to make every effort. The shifting to the 'P' gear only produced a crackling noise without having any suppressing effect on the speed of the car.
I again shifted the gear to the 'N' position while the car was still moving at a very high speed and the only thing which came to my mind at that moment was to close down the ignition and take out the key,which could finally bring down the speed as the brakes did not seem to work. All this time I was following a jeep which was fortunately making my space for the maneuvering of the car on a busy street but when I realized that my speed was exraordinarily high ( without pressing the accelerator pedal ) and I could bang into the jeep which was moving in a normal speed, I found a vacant space on my left where I thought I could dash my car to finally stop it. I did the same and finally, succeeded in stopping the car.
Taking out the keys would lock my steering wheel did not come to my mind at that time but it also did not hamper in my maneuvering the car during this ordeal.
The entire episode took hardly around 30-40 seconds wherein,I experienced the shock of my life but ultimately,I came out of the car unhurt.
The car had dashed into an angle iron demolishing a boundary wall and was standing still with its right rear wheel off the ground. To check if the brakes were really not working, I turned around the wheel with my hands and applied the brakes, and to my surprise,once again,the brakes did work and the wheel stopped.
WHAT COULD THEN BE THE CAUSE OF THIS MISBEHAVIOUR IS A BIG QUESTION?
Your expert opinion would be a great relief.
PLEASE do respond to the query.
Waiting for your prompt reply,
Yours truly,

DUA40