Did you notice whether the anti-theft light on the dash stayed lit or if it went off while trying to start it? Please try a simple relearn procedure which will reprogram the key to the security system.

Have you used Scanner to test it? Is there any fault codes. Check the timing belt.

 What timing belt have to do with this issue???? 

We are not professional vehicle technicians, but you can check your car as following troubleshooting ways:
Possible reason:
Engine idle control not good——
1. You can try to increase the engine RPM, if it doesn't stall, then the previous stalling may be caused by the lower idle speed. So you can check the engine ignition system, timing belt, fuel-supplying system, like Ignition Coil, injector.
2. If increading the engne RPM, it still stalled, then it maybe the problem in transmission. Check gear switch, input shaft speed sensor, Transmission Oil etc.

 You need to back up here.  Was the car doing this before you applied the scanner?  When it shuts off, are all of the dash lights coming off?  Need to give a little more background here and what you are trying to accomplish and which tool are you using.

Maybe a problem internally with the transmission  range sensor or  when engine trans axle movement causes a ground to be lost or harness movement causes a wire to chaff through against a bracket.