If the laptop won’t power on when you using the AC adapter alone, maybe you have a faulty charger, you have to check it.

How to test AC adapter with multimeter:

To test the AC adapter, first you have to unplug the AC adapter cable from the Laptop.Measure the output voltage at the plug of the AC adapter cable. See the following figure:

Note:

Output voltage for the AC Adapter in picture may differ from the one you are used. If the voltage is not correct, replace the AC adapter.

If the voltage is acceptable, check the power jack and the laptop motherboard. in most case the power jack fail or electronic component directly after power jack fail.