Laptop Charger Failure during AC supply undervoltage
A laptop adapter is typically based on a switching converter, maybe a PFC front end and an LLC DC-DC regulator.  

That means it is a constant power load.  As input voltage goes down, current goes up.  

As current goes up, conduction losses (I^2R) increase.  In a properly designed charger, an under voltage condition will not cause damage due to several safeguards built in.  

Usually there is an under voltage lockout which shuts the converter down if the input voltage is too low, and a thermal shutdown which shuts the converter down before damage occurs.

Does your charger start to work again when it cools off?