Why is my car dying while driving?

I have a 2003 elantra and have recently had issues with it. Over the course of the past few months, it has stuttered and slowed to a stop while I was driving and then not started for a few minutes following the incident Without fail, if I wait 5-10 minutes and try to start my car again, it will turn on. Today, it escalated. After driving over 250 miles, my steering wheel locked and my car started to slow then die. A mechanic pulled over to help me and was not familiar with my model of car, but said it seemed to be an issue where the engine was not registering that fuel was in the car. (Jump start and starter fluid did not work). I'm supposed to drive another 300 miles tomorrow and I don't know if I should take the car in or hope for the best regarding the drive. Anyone know what it could be and how much it would cost (and how long it would take) to fix such a problem?