My MacBook Air keeps randomly shutting off on me and does not show battery status.

When this first started happening, it would only happen when I would use skype. Then the other day I was on youtube and my computer completely shut off on me out of no where. I had it plugged in to the charger, and after it shut off from being on youtube, it completely stopped working. My charger wont work with my mac anymore. The light doesn't turn on, and it doesn't show up as charging. ALSO, the battery status has completely vanished. When I look at my battery health and status, it says that it's not charging and that I don't even have a battery. My fans are also on HIGH SPEED and will not stop. & my keyboard light is not working anymore. Do I go to the Apple store and ask for a new battery? Has anyone else ever had this problem?

I also noticed this started happening when I installed Mountain Lion version 10.8.2. Not sure if that has anything to do with it.