The only real test is to try the adapter on another Dell system.  If it produces the same error on that system, the adapter is bad.

If it does not, then the problem is with the DC jack in the system - or less likely, the mainboard.

If you don't have another system to try, see if a local shop does - or has another adapter you can try.

I have tried my laptop with another new adaptor and it did not give me the same message, do that mean the problem is with my motherboard?

Is there any way to check whether my laptop is running in high or low performance mode? Cause i really feel that my laptop is under performance. Thanks so much.

Thanks so much on answering, but i wonder how i know my adapter is recognised after pressing f2?

There will be a screen that shows AC adapter followed by either its wattage setting (65W, 90W, etc) or "unknown".

If it's "unknown" it's not being identified.

It depends on whether that was before or after you suppressed the message with F3.

With the new adapter connected, go into setup (F2 at powerup).  If the adapter IS recognized, the problem was the original adapter.  If it is NOT recognized and IS a Dell adapter, replace the DC jack next.  In most cases the faulty part is either the adapter or the jack.

If neither replacement (of the adapter and jack) solve the problem, then the mainboard is bad.

The system will run at battery speed unless the AC adapter is correctly recognized.