Warning:the battery not recommended for this system,the system will not be unable to charge this battery

System model?  Age of system?  Does the system correctly recognize its AC adapter?

my system model ( Xps502x ) the i don't know if you ask about how many years i used but its more 5 years ,and this the ac adapter orginal. But i think he not recognize it

But how the peoblem with power jack ana the laptop working with charger but not charge the battery?

If the adapter isn't recognized, the battery won't charge.  And if you've already tried another Dell adapter, to no effect, the power jack would be next to replace:

www.parts-people.com/index.php

If that doesn't solve the problem, it's the mainboard that is faulty.

There's a center pin that completes a charge circuit - it is entirely possible for an adapter to power the system but not charge the battery.

You prefer to try new power jack if not working then the problem in motherboard?

Note: my old battery ( 6% plugged in and not charging)

New battery (100% charging ) and the light sign

The next unanswered question:  is this a Dell battery or a third-party one?

If the AC adapter is not recognized (verify with F2 - setup), and you've already tried another Dell adapter with the same results, replace the DC jack.

That should solve the problem.

If the AC adapter IS recognized but two batteries are not, chances are the mainboard is at fault.

Dell battery

As you mention already having tried another adapter, replace the DC power jack next.

I see in bios AC ADAPTER :unkown