Charger polarity inverted by mistake

Not sure if your charger is the type that shuts itself off, when something is wrong.

Does the charger have a status light ? Does it come on when you plug it into the wall ?

If not, the charger may be dead.

In any case, remove the laptop battery. Do not leave it in the machine.

If its over 2 years old, I recommend a replacement.

Try- With the battery out, plug in your charger. Will the laptop power-up ? Are any lights ON ?

The charger (assuming it still works) will power the laptop without the battery. Usually, the battery light will show red/yellow/green. PowerOn/Charging/BatteryGood/Bad

If it works, you're happy, all you need is a new battery.

If it does not work, take laptop, dead battery, and charger to the serviceman. There are several tests that can be done without dis-assembly. Before you D.I.Y. ( Do It Yourself ), search the web for "samsung laptop how to". You will find several YouTube movies.