I don't think he means nothing happens... I don't think anyone would be persistant enough to attempt to start it 15 times if nothing happened at all. I highly doubt the starter, assuming the starter is turning over the engine (otherwise your post would have been "I hear a sound when I turn the key, but nothing happens to the engine" in which case, you wouldn't have had any doubt. Also, the alternator doesn't have anything to do with it not starting. Plus, if you can turn it over 10 or 15 times before it starts, I doubt it's the battery - if the battery was too weak to start the car in the first place, you'd only hear a clicking sound long before you hit attempt #15.
However, I have no idea what the problem is... Definitely get a clean air filter in there, certainly can't hurt, and it's pretty cheap.