Mac Shows that charger is connected even though its not. Battery percentage shown is wrong. How do I fix this?

Hi,

I have a 13-inch early 2011 MacBook Pro. Recently, the 65W charger that came with the mac stopped working. It took me a while, but I found what appears to be an original Mac Magsafe charger.

When I plug this charger in, the macbook charges, but when the charger is removed, the macbook still says that the battery is charging even when it's not. So even after using the Macbook for a few hours, it still shows that its plugged into the charger and that the battery is a 100%. But when I check the battery by clicking the little button on the left hand side of the macbook, the LEDs show me the real amount of battery left.

I have tried restarting Macbook several times and even tried an SMC reset, but it still shows the computer as plugged in.

How can I see the real status of my battery?

Is the charger causing the Macbook to do this?

Thanks for you help!

Regards,

Arjun