The starter is an electric motor that consists of several brushes. These brushes carry electrical current that allows the motor to spin and therefore turns over the engine. Sometimes one or more of these brushes "burn" and don't allow any electrical current to pass thru them anymore. If the starter motor is already spinning, most likely it will continue to spin even if it reaches one of the "burnt" brushes and the car will start with no problem. However, if when the starter motor stops spinning, it lands on one of the "burnt" or faulty brushes, the next time you try to start the vehicle, there will be no way to carry the electrical current and therefore the engine will not crank over. Many times after repeatedly turning the key on this will bump the starter past the bad spot and allow it to start. Why did it start when you jumped the battery? Because instead of the normal amount of current going to the starter (which is not enough to overcome the bad spot), you have doubled the amount of electrical current going to that motor which is enough to overcome or "jump past" the bad brush and get the motor spinning. Like I said before, once it is spinning, it is likely to continue spinning even when the bad brush or brushes come back around in the rotation. You need to find a shop that can perform a battery, charging and starting test. Plus you should also be willing to leave the car with them until they can duplicate the problem. You mentioned you have had the problem twice, but in how many days? If it doesn't occur every time you try to start the vehicle, it will be harder to determine for sure the exact cause. If they can duplicate the problem you are experiencing, they can run further tests and be sure the correct part is being replaced.