Could very well be the starter, too. If you're jumping it with a good battery then maybe it's giving the solenoid in the starter an extra "boost" that gets it going. I've also seen loose terminals that won't supply enough contact to get amperage to the starter, but when someone jumps the vehicle it squeezes the terminals enough to make that contact. If you jump it, it runs, and then shuts off after the terminals are taken off then likely it is the alternator. Go to Advance Auto Parts or any other auto parts store and they will do a system check, checking your battery, starter, alternator, and for any amperage drains all in one go.