2003 Hyundai Sonata Fuel problem or engine?

Hi, Thanks for your question. I need a clarification, when it does not want to restart, is the motor still somewhat warm? If this is the case, and it starts fine when completely cooled( when the computer calls for fuel enrichment) I would suspect failing intake gasket. Many times this is the culprit, and can be hard to detect in the shop bay. Once the engine has started, engine vacuum can pull the intake tighter and mask the problem. With the engine warm and off, use a spray bottle with a little dish soap and water and liberally spray the area where the intake and head meet, and immediately attempt to start. If it starts right up- you have found the source. Hope this helps, Doc