It's possible that there's a short in either the charger, or the charging port on the laptop.
I would first check to see if you can borrow a cord from somebody that has a similar model and see if it works fine that way.
You could also try checking your temps (Use this: CPUID - System & hardware benchmark, monitoring, reporting
) while your computer is on and see if the temps are high. But I'm leaning towards something wrong with the charger or port.
Also, is the charger able to wiggle around when it's plugged into the laptop? Or does it plug in firmly and not move?
You could also try using a digital multimeter and test what your charger is outputting for voltage/amperage. If you don't have a multimeter, you could take it down to a local computer or electronics shop and ask if they could measure the voltage/amperage output and compare it to what the label says its supposed to output.