Could be several things. But you only need three things to run, fuel, properly timed fire, and compression. If it died out like it did though, I would guess either fuel or fire. Did you car turn over when you turn the key? If so, then most likely it is not your alternator because pretty much all your alternator does is keep the electricity running to your car and charge your battery, basically meaning if the alternator went Ka-put, then the car would run off of the battery til it died and then your battery would be dead as well. So I am assuming that your tried to start it after it died, and it was turning over, just not starting. The first thing I would check for is spark as that is pretty easy to check, just pull off one of the spark plug wires off of the spark plug, shove a screwdriver in the boot so it is touching the metal inside and then holding the spark plug boot or better yet, positioning it in a manner that the metal of the screwdriver is really close to a ground area of the car without touching, have someone crank it over to see if you see a spark. Other variations would be to remove a spark plug or use a spare spark plug and put that in the spark plug wire and then the part of the spark plug that you thread into the head, you touch that to a grounded area of the car, have someone crank over the car and you should see the spark, or use a tester made to check for the spark, or even a timing light. If you dont get spark, then there are a lot of other steps to go through, if you do, then check for fuel, maybe your fuel pump went out. Let us know where you are at after you did this, and I can give you several more tips what to do next.

Hope this helps, Good Luck!