I just bought a 2001 Hyundai XG300 that is supper clean and nice with only 66k miles. I drove the car a lot before I bought it. I turned it off and on several times. Overall the car checked out. The day after I bought the car, I went to the store (car barely had time to heat up). When I went to get back in the car it would crank but would not start. I cycled the key and it started. Didn't think much about it. Went down the road to another store and this time when I returned to the car it would not start (it would crank just not start). I had the car towed to my mechanic and the next morning he went out and started the car right up. He could not get it to replicate the problem. I had him go ahead and replace both the pump and fuel filter (the filter was DIRTY). I picked the car up and drove it that night turning it off and on several times with no issues. The next day drove to work. When I went to leave work about 7 hours later, same issue! The car would crank but would not start. Mechanic had it towed back and again the next morning the car started up. Mechanic has had the car a few days now and still has not been able to recreate the problem. The car has not set any codes.

 

Did you get the problem fixed? I am having similar issue.