Had this SAME thing happen to me and it was an easy no cost fix. In my situation, before it had the start/ idle problem, the battery was disconnected during a front end collision repair. After driving for a half hour or so it did the same thing. It would not start or stay idle. I did some research and found this to be a common problem when disconnecting the battery. I was instructed to go through an "idle re-learn", which essentially is teaching the ECU to keep the idle at where you want it. Other wise it will not keep an idle. What I did was turn the car on and had my foot on the gas a little. Then I just kept it at about 800rpm for about 5-10 minutes by applying light pressure to the gas pedal. After I did this, it stayed right at 800. Never had an issue since! Your case may be different though, just wanted to share my experience with this issue! Thanks!
