Create a [https://www.windowscentral.com/generate-battery-report-windows-10|Win 10 battery report] to check the status of the battery.
Compare the ''Design Capacity'' to the ''Full Charge Capacity'' values in the report.
If there is a big difference it may be that the battery is failing and the charger cannot do both, i.e. run the laptop and charge the battery at the same time.
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=== Update (01/14/2021) ===
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Hi @Rasmus Lorenzen
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The battery is only at 72% effectiveness when fully charged but I would have thought that even at this value it should be able to start the laptop without the charger connected, unless it is faulty and cannot handle the load.
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Since you have changed the charger cable and measured the voltage at the input to the laptop the only way to tell now is to replace the battery as then you will know that you are using a known good battery.
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Here's the [https://download.lenovo.com/consumer/mobiles_pub/lenovo_y40_50_series_hmm.pdf|hardware maintenance manual] for the laptop. Go to p.36-37 to view the necessary pre-requisite steps and then the procedure to remove/replace the battery pack.
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On p.91 Item #14 you will find the part number for the battery.
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Search online using ''only the part number'' appropriate to your particular model variant to find suppliers of the part.
Hi,
Create a [https://www.windowscentral.com/generate-battery-report-windows-10|Win 10 battery report] to check the status of the battery.
Compare the ''Design Capacity'' to the ''Full Charge Capacity'' values in the report.
If there is a big difference it may be that the battery is failing and the charger cannot do both, i.e. run the laptop and charge the battery at the same time.