It seems your Web Application Authentication settings got corrupted somehow. You can try to clean this up by simply Enabling and Disabling Anonymous Access.
You can do this by
- Open Central Admin Site
- Open Application Management & Select Manage Web Applications
- Select web application in question and open Authentication Providers
- Choose default authentication provider zone
- Check Enable Anonymous Access and Save
Now do the same steps as above and in step#5 - Uncheck Enable Anonymous Access