Starting System Problems:
* Bad Starter Motor: This is a very common culprit. A jump start might temporarily give it enough power to crank, but it might not have the power to fully engage or spin the engine fast enough to start. Symptoms include a slow crank or a clicking sound when you turn the key.
* Starter Solenoid: This is the electromagnetic switch that activates the starter motor. A faulty solenoid can prevent the starter from receiving power, even with a good battery and starter. Clicking is a common symptom here, too.
* Ignition Switch: A failing ignition switch might not be sending power to the starter even when the key is turned.
* Wiring Problems: Corroded, loose, or broken wires in the starting circuit can interrupt the flow of electricity. This includes wires connecting the battery, starter, solenoid, and ignition switch.
* Neutral Safety Switch: This prevents the car from starting unless it's in Park or Neutral (automatic) or Neutral (manual). A faulty switch will stop the starting circuit.
* Faulty Alternator (unlikely but possible): While the alternator charges the battery *while the engine is running*, a completely failed alternator *might* not be charging enough when the engine is running briefly after a jump. This would be less likely in the immediate period after the jump.
Parasitic Drain (Battery keeps draining):
* Internal Battery Short: Even a new battery can have an internal short, continuously draining its charge.
* Parasitic Drain from Accessories: Something in the car's electrical system might be drawing power even when the car is off. This could be a faulty radio, interior light, alarm system, or other accessory. A multimeter is needed to diagnose this.
Troubleshooting Steps:
1. Check Battery Terminals: Ensure they are clean, tight, and corrosion-free.
2. Listen Carefully When Cranking: A slow crank, clicking, or grinding sound will point towards starter or solenoid issues.
3. Check for Obvious Wiring Issues: Visually inspect the wiring related to the starting system for damage or corrosion.
4. Test the Starter (with a professional or with a multimeter and experience): This requires some electrical knowledge.
5. Test the Battery: Have the battery tested at an auto parts store to see if it's holding a charge.
6. Test the Alternator (after a successful start): Ensure the alternator is charging the battery.
If you are not comfortable working with car electrical systems, take it to a mechanic. They have the tools and expertise to diagnose and repair the problem efficiently and safely. Jumping the car might temporarily mask the problem, making proper diagnosis harder.