The car just refuses to start when the key is turned..

these cars are very expensive and complicated when something's wrong, so I feel for you. A check engine light does not have to be on for a mechanic to diagnose a car. It does point in certain directions which can be helpful. I'd like to see them start your car no problem after you've had no luck getting it started. Proper startup procedure would be for you to keep your foot off the accelerator pedal when you're starting it, unless the weather is very cold an you need to give it a LITTLE gas under cold conditions. I'm wondering if you're pressing the pedal down when you're starting it, if you press down much on the pedal the car thinks you're trying to clear a flooded condition and cuts off the fuel. Just a longshot. Keep your foot off the pedal when starting in normal conditions. I've seen lots of people having startup problems because they put the foot down on the pedal too far, it's not gonna start that way.