Hyundai Repair: intermediate starting problems, crankshaft position sensor, definitive diagnosis

Question
My 2003 Accent has developed an intermediate start problem.  The car will crank but not turn over.  Jumping does not work. the battery is new. When I have the car towed to the mechanic it starts up fine. I take it home it works fine then 3-4 days later I go to the store come out and nothing. The last time left me stranded for 1 1/2 hours waiting for a tow. From my internet research it seems to be happening to thousands of owners and yet no one has answers.  Do you.  My best guess is a faulty sensor.

Answer
If I had to hazard a guess, I'd guess the crankshaft position sensor.  When this fails, it will typically leave a P0335 diagnostic trouble code (DTC) in the engine control module (ECM).  Do you know if the mechanic checked for trouble codes?

If there are no codes stored, it's difficult to provide a reasonably definitive diagnosis without being able to run diagnostic tests while the problem is occurring.  Tests run while the car starts normally will provide normal results.