Engine shuts off while driving at any given time or speed and is an intermittent and unpredictable problem

Car shuts off while driving yet the car battery remains powered. This occurs intermittently and at unpredictable times leaving the driver without steering or brakes at any given speed while driving. If an attempt is made to restart the car immediately after the car shuts off, it responds as if the timing of the engine is seriously out of place; wait a few minutes and the engine starts. This can accrue during a long drive or not at all or several times within a mile. This is a sudden loss of power and is not a fuel problem. I am fairly sure it is not an anti theft issue. I am suspicious of the Ignition control mo dual or the on board computer. This problem started immediately after a AAA person was called out to test my dead battery. He jumped and started the car but said the battery needed replaced and I replaced it. When I went to start the car he It would not start but acted as if the timing was off. He told me to wait until the on board computer cycled through its program. Fifteen minutes later it started and I drove the car seventy five miles home. My cruise control kicked off two or three times during that drive. This lead me to believe the problem is in the ignition control modal because of the changing out of my battery. The problem reoccurred the next morning within a mile or two of my house and so I return home. I checked the battery and the positive terminal was never tightened down. It was loose. I was also suspicious of the fuse box which the battery guy unbolted and moved to get the battery in and out. I did the changing of the battery in the dark with the light from his cell phone. A really poor job he did. I think he messed things up. I have avoided longer drives. The problem so far has occurred once again. Wait a few minutes and it starts What is your opinion of this problem? I would appreciate your thoughts. Sincerely, Raymond Johnson.