Problem:

Error - You must be running under a password protected Web Server to use EnterpriseLink Project Management functions.

Resolution:

The confusion is that "Web Site" password permission doesn't matter its' the "Default Web Site" that needs to not be anonymous in IIS

Go to IIS Manager

Local Computer -> Web Site -> Default Web Site

Right click ->  Properties -> Directory Security -> Edit

Unclick   "Enable anonymous access"

Click on "Basic authentication"

Restart the IIS server and that should do it.