do a fuel pump pressure test,to make sure it is getting enough fuel,make sure the plugs is getting a good spark,is the starter turning the motor over fast enough,you could also check FOR a bad sensor.good luck
I would NOT go back to that mechanic... That's there job to figure out whats wrong...
There are 3 things that a motor needs to run..
it has to not have one or more of those to not run. A simple test should provide that info...
we know its getting air,
is it getting spark at the plugs ( pull a wire off and put a screw driver in the end and hold it near a bolt and have someone crank the motor does it spark.. if so then that's OK..
is it getting fuel.
There is an immobiliser on these cars from what I understand, if the battery went bad, or disconeccted that could have told the ECU that something was wrong and will not allow the car to start until it is reset.