One problem related to transmission not engage has been reported for the 2004 Hyundai Santa Fe. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2004 Hyundai Santa Fe based on all problems reported for the 2004 Santa Fe.
On purchase of my vehicle, Hyundai sante fe, the car has had troubles. I have had it back to the dealer multiple times since I purchased the car with the same complaint. When starting the car and pulling out from a stopped position the car hesitates 3 to 4 times before driving smoothl. It feels like the car is bucking or hesitating. . . . I have had it to the dealer atleast 5 times since it's purchase. They can not duplicate the problem. I have told them specifically how to get the car to do the problem however they do not follow my instructions. The car needs to be pulled out of the parked position with force. (as if pulling into a high traffic area out of a parking spot) it occurs more offen when the car is cold, but also makes the same hesitation if the car is warm. However, never after the intial engagement while driving. It does not happen while parked at stop light while the car is running. It occurs when initially turning the car on. This problem has not lead to an accident to date, however it could if not resolved. If pulling out into a high traffic area and the car does not engaged and get up to speed, I can see being hit by another car.