This 2013 MBA works fully with the exception that it does not charge.  I have tried a new charger and charge port but no luck. When the battery has charge, the laptop works as normal.  I do not know why it does not charge. The charge light does not come on when connected.

The battery installed has been drained and as a result,  the laptop no longer turns on. Again, while with a charged battery the computer works fine, please note that it does charge. For parts/not working.