My backlit keyboard problem is solved! I just got off the phone with a product specialist at Apple. He had me shut the computer down and unplug everything including the power cord. I then held down the power key for about 15 to 20 seconds until a loud beep was heard. He then had me let go of the power key and let it boot up normally. Once it came back on, the backlit keyboard was working properly. As far as the long battery charging issue, he said to let it completely drain and then recharge again. He said that would help calibrate the battery. We'll see.