Battery / AC adaptor for laptop ES1-512 low end version

Hi to all. My daughter laptop stop charging a few weeks ago. I tried to restore the battery with pin hole but It doesn't charge anymore. The ac adapter is the original one. Since battery is incorporated my question is can the laptop work with ac adapter plugged in all time? How to do that? Or does the MB have a circuit to avoid this in case battery fails? Perhaps removing battery? At the moment I have no spare part that's why I need to know.
Thanks.

Btw if ac adapter is plugged no light nor power on cycle

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Laptops work normally without the battery so it should start and work as normal.
If it doesn't start - battery is not the problem,

What pinhole do you refer to?

 

You think it may be the MB? The pin hole is right below the laptop with a better y icon removed. Since the battery it's embedded I cannot just unplug it. But I left.it days connected after checking power ac and nothing...if you have any steps I may follow to diagnose the issue I will appreciate it. Thx

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You would have to disassemble the laptop to remove or disconnect the battery which is not that hard - there are YouTube videos showing how to do that - but in my opinion it won't matter. The notebook should work even if the battery stopped working, so I don't think it's the issue. Can't say if it's the mobo or something else.

Is the PSU definitely working alright?

 

PSU is ok. After some checks I concluded it's the Mobo. Will now look if its possible to find some replacement. But In this cases new it's better I guess. Thx for the help.

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