A friends car didn't start, no clicking noise?

Well at first the car had trouble starting but we took it anyway after it finally started. Then when we were about to leave our destination, the car wouldn't start. We tried messing with the battery, push start, but nothing worked. The noise it made when turning the key wasn't a clicking noise that's usually attributed to a poor battery, but sounded like it was coming from the fuel pump or something. Well, after an hour of just sitting in the lot trying to start the car, we finally decided to call the insurance company and minutes later the truck arrived. Five minutes prior the car wouldn't start still, but when the tow truck driver came the car started. We then wondered how and the driver was dumbfounded because he came to fix a non-working car. We turned the car off to see if it started and the car successfully starts every single time. What gives? It was a 2002 Toyota Camry. The car is running now and he took the car to a friend to fix "something". What do you think happened with the car? Why am I asking? Because I know nothing about cars and I want to get some knowledge of it. I also figured it's some sort of a thing I should know if it were to happen in the future.