assuming the new charger is a genuine one not a fake and is working then it is likely that the 'power in socket' is faulty
There are a lot of cheap fake power supplies on market which are electrically unsafe, put out unregulated or too high voltage and cause more problems
On many laptops the connector is directly soldered onto the motherboard and requires a skilled person to disassemble, re solder and re assemble the laptop.
You need to find an expert who can check this out for you.
(It could be fault in charging circuit but less likely)
This problem usually occurs with people who pull the charging cable tight straining the connector
It is not too difficult to check the original and new power supply is putting out correct voltage typically 15V to 20V