Car wont stay running?

Do you have an aftermarket alarm system installed? If not then check to see if a security light is coming on when the engine stalls? Are there any codes in the vehicle's computer? The crankshaft sensors can cause different no start issues when they go bad. I have also seen the TPS sensor cause this issue.

For no start conditions you need to rule out some systems. I would check for spark. Get a spark tester from any automotive tool supplier and test or you could use a screw driver inserted into the spark plug boot and held close to the engine with someone trying to start the engine (**Take care to get electrocuted if using a screw driver). Crank the engine for about 15 sec and make sure your getting spark consistently through out those 15 sec.
If the ignition systems if proving out good
Next, check for fuel pressure with a fuel pressure gauge. 3.1l engine fuel pressure 41-47 psi 3.8l engine fuel pressure is 48-55psi. If this is good, next you'll test for engine timing and then compression. Hope this helps and good luck. If you have any questions let me know, Ty

If you want to rule out an open purge valve (causing a large vacuum leak) just disconnect the pipe connected to the intake and plug the hole preventing any vacuum leaks. This purge line is the only thing that can cause a no start every thing else the "EVAP" system shouldn't cause a not start condition just increased emissions.
Tampering or bypassing emission components I believe is a federal offense. But for testing it should be ok just as long the emission components are brought back to original working order.
Hope this helps, TY

Your welcome happy to help!