2000 suzuki station wagon

My daughter has a 2000 suzuki station wagon that has about 60k miles on it. Intermittently the car will not start, especially if it has been driven in the hot Arizona sun. She has had the vehicle maintained consistently, and recently paid about $700 for repairs including oil pan gaskets, steering fluid leaks, etc. But the starting problem was not solved. The mechanic stated that there is a sensor on the back side of the engine that monitors the speed of the engine and if that is bad, the engine will start intermittently and at some point the engine will not start at all. The cost to simply check the sensor is about $1000 because the engine has to be pulled to get to the sensor. Is that a correct diagnosis or are there other possibilities? We have checked all the other normal problems, like battery terminals, loose wiring, and the starter motor itself - all to no avail. Please help!