Hyundai - Santafe :: 2004 - Random Starting And Accelerating

My 2004 Hyundai Santa Fe with 78K miles has never had any major problems until a month ago. I was doing errands and after my second errand the car would not start. AAA came jumped it, and I took it to a local shop where they replaced the battery. They said the rest of the car seemed just fine. The next week, after gassing up, the car again would not start. It made the same sound, like the engine was trying to turn over or it wasn't accessing the fuel. A bystander thought perhaps it was the oxygen sensor.

After resting for about 10 minutes, the car started and I drove it to a Hyundai dealership. They said the fuel pump needed to be replaced. It seemed fine after the replacement. A week later, the same thing happened. The car would not start. Not after 10 minutes, not after 30. AAA again was called and after I told them about the fuel pump they thought perhaps the relay was bad. They swapped the relay with one I wasn't using and the car started.

I, again, brought the car to the dealer. They inspected the whole car. There were no codes when they hooked it up to the computer and it drove just fine. They simply replaced the relay. Last night, the car made a funny sound upon starting, almost like a hissing or light clunking. This morning the car started fine. I drove for about 5 minutes and then the car stopped accelerating and the power steering seemed off. The car then died and would not start. I was in the middle of an intersection.

After about 15 minutes the cops came and pushed my car while I was in neutral. A few minutes later the car still would not start and it was towed back to the dealer. The car has been with the dealer for over 3 hours. They have driven it, tested it, driven it, tested it while driving. Everything. And they can't replicate the problem.