320Ci won't start

Just got a 2002 320Ci this week, low mileage 37k, full service bmw service history, everything was perfect for last few days, but came out this morning and wouldn't start, left it as i had to go to work but
came back at lunch and it started fine and drove it around for the day
not sure how immobiliser works but people said to me it was probably that
however this evening the same thing it wouldn't start...after a while i opened it with the key which sets off the alarm and it started so i thought great but i left it run while i locked up the house and it cut out after about 30 seconds now it won't start....i didn't rev the engine after it started....did i flood the engine ttrying to start it? Any help appreciated! bit of a dummy when it comes to cars

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