Why is my fan on full blast upon turning on my macbook pro, and why is my battery/power acting weird?

My laptop has been acting really weird the last couple of weeks. Recently, when the Power adapter is plugged in, the LED light won't light up, and my laptop won't charge, after putting it back in a couple of times, it finally does. When my laptop is plugged in, and then when the LED light goes dead, my whole laptop shuts down, even though there is some battery life left. This causes my computer to lose the date and time, which I have to reset. It did this again today, and now my fan is on full blast nonstop. The battery icon on the top right has an x through it, and it says there is no battery available, however it recognizes when i put the non functional power adapter in, as the power source says: power adapter. I've had my macbook pro since 2010, but I've never had these kinds of problems. Any help is appreciated.