Starter will not engage. have new battery. sometimes car starts. sometimes not. when it won't start, jumping will start it. mechanics can't find the problem.

Try cleaning battery terminals

might be a burned spot on the starter contacts where the brushes power the motor.
tap the starter to see if problem goes away.
sometimes you can clean the contacts but that is a temporary fix.

sounds like starter solenoid

It is probably your cellinoid try jumping your starter

Could be a failing starter or problems with the cables.
A dead cell in the battery will do it too.

Replace the starter motor.

Grab a test light go down to the starter, hook to a good ground and probe the battery cable. If that has power probe the solenoid engage wire( its the little one) have a helper turn the key to start if that gets power replace the starter.

That symptom usually means the solenoid on the starter is bad and no longer is completing the circuit to engage the starter. A new starter will likely solve that issue. A series of rapid clicks would indicate a week battery. You can try repeatedly turning the key to the start position rapidly, sometimes the starter wil start working. You can also try tapping the starter while somebody holds the key in the start position, if the starter engages place it.

I’m happy to assist further over the phone at https://www.6ya.com/expert/jeremy_d728a59f986299fa

We had the same issue on an 2001 Aurora. I left it for a year before it finally annoyed me enough to fix it. In our case it was the starter. The only difference was we didn't get a click of the solenoid when it happened.
I would guess the starter OR the alignment of the starter. If the starter is not aligned properly, sometimes when the solenoid engages it does not throw the gear out into the flywheel properly.
The "starts with a jump" doesn't make any sense to me. If this is really the case I would look at the battery and connections for an issue. If you do not have enough power to engage the starter properly this could be the issue.

Return the battery and get another, sometimes because the battery set there too long and won’t work, I had twice when I had my Union 76 Station, after you try it, if you still can not start your son’s car. Let discuss more.