2001 Honda Accord electrical system problems

My mother had picked up my niece from her school and was waiting for my nephew and his friend to get out of high school. When ready to go, the car was difficult to start. Took about 10 min to get the car to start. After the car started, went into reverse and backed out of the parking space. Put the car in drive and it "chugged" a couple of times. Then the car accelerated unexpectedly. She was unable to slow the car down by applying the brakes.

Horn functions intermittently. While driving straight ahead (normal highway driving), horn does not work. Isolated the malfunction and found that the steering shaft is only intermittently grounded, and the horn requires that ground in order to function. The horn (and the steering shaft ground) operates perfectly when the key is removed from the ignition switch. It appears that something in the ignition switch is causing the loss of ground. The failure has not been repaired as of yet.