I wouldn't say your power supply / charger is in the clear until you've tested it under load, say with a laptop model similar to yours that it is compatible with. It might look fine with a multimeter but croak under load. Trying another known good power supply if you can would also help confirm whether yours is good or not.
If you're up for taking your laptop apart, you could dismantle it enough to access the connection of the power jack to the motherboard and see if it looks good visually and probe it with a multimeter. You'd be looking for DC voltage / amperage within the spec range for the supply (should be printed on the power supply somewhere). Beyond that, I think it gets tricky and you'll need a fairly extensive electronics background. Maybe you'll get lucky and you'll find a broken trace which you can repair with a lead pencil or trace repair pen, but if the fault is in a component somewhere, even if you were to find it, removing and resoldering surface mount components takes specialized tools and a skilled set of hands to operate them.
Also, it sounds crazy, but check this out. Maybe try updating your BIOS?