My honda won't start. I jump start it and it turns on but then turns right back off. I push started it and it would turn on but then turns off faster. I jump started it longer then it stayed on longer. But still eventually turned off...
Before when the car would run. The engine sounded perfect. I don't know what could be wrong. I'm thinking the alternator.

If the starter motor does not crank:

https://www.askmehelpdesk.com/cars-trucks/faq-how-troubleshoot-repair-maintain-hondas-selected-other-vehicles-46563-3.html#post235560

Jump starting increases the risk dramatically of a voltage spike damaging the ECM, alternator, or sensors. It's best to remove and fully charge, or replace, the battery. Most auto parts stores will test and charge batteries for free.

If the ignition switch isn't acting right, check it for wear, pitting, or melting:

https://www.askmehelpdesk.com/cars-trucks/faq-how-troubleshoot-repair-maintain-hondas-selected-other-vehicles-46563-2.html#post224652

Most likely the alternator, basically the battery is used only to start the car and the alternator keeps it running. Be sure to fully charge the battery if you replace the alternator otherwise you may overheat and damage the new alternator.