Fans die. Especially case fans. My exhaust fan died a few months ago and I had no idea, until the day my computer kept shutting down during games because of overheating.
Easiest way to check if a fan is dead is to, obviously, look at it when it's on. I'm guessing your case fan is dead - find out the size, head to Newegg.com or your case manufacturer's website, and get a new one that fits. Installation is relatively simple and you'll be up in no time.