How to disable windows authentication for WEB API inside an ASP.NET MVC 3 application

I have an ASP.NET MVC 3 application with Windows authentication. Now I've added the web api to it (nuget package) and want anonymous access (later on I'll add an api key). But I haven't managed to get it to work.

All my WEB API controllers are under the "/api" path, and none of them have the Authorize attribute.

Here's my current web.config (I removed all the bits and pieces that are irrelevant to this matter):

<?xml version="1.0" encoding="utf-8"?>
<configuration>
  <system.web>
    <authentication mode="Windows" />
    <httpRuntime maxRequestLength="102400" requestPathInvalidCharacters="&lt;,&gt;,*,:,&amp;,\" />
    <authorization>
      <deny users="?" />
    </authorization>
    <roleManager enabled="true" defaultProvider="AspNetSqlRoleProvider">
      <providers>
        <clear />
        <add name="AspNetSqlRoleProvider" type="System.Web.Security.SqlRoleProvider" connectionStringName="..." applicationName="..." />
      </providers>
    </roleManager>
    <profile enabled="false" defaultProvider="AspNetProfileProvider">
      <providers>
        <clear />
        <add name="AspNetProfileProvider" type="System.Web.Profile.SqlProfileProvider" connectionStringName="..." applicationName="..." />
      </providers>
      <properties></properties>
    </profile>
    <customErrors mode="RemoteOnly" defaultRedirect="~/Error/Generic">
      <error statusCode="404" redirect="~/Error/NotFound" />
      <error statusCode="403" redirect="~/Error/AccessDenied" />
    </customErrors>
  </system.web>
  <system.webServer>
    <validation validateIntegratedModeConfiguration="false" />
    <security>
      <requestFiltering allowDoubleEscaping="true"></requestFiltering>
    </security>
  </system.webServer>
  <location path="Error">
    <system.web>
      <authorization>
        <allow users="*" />
      </authorization>
    </system.web>
  </location>
  <location path="Scripts">
    <system.web>
      <authorization>
        <allow users="*" />
      </authorization>
    </system.web>
  </location>
  <location path="Content">
    <system.web>
      <authorization>
        <allow users="*" />
      </authorization>
    </system.web>
  </location>
  <location path="api">
    <system.web>
      <authorization>
        <allow users="*" />
      </authorization>
    </system.web>
  </location>
</configuration>

All my requests are getting "HTTP Error 401.2 - Unauthorized", but when I enter some valid windows credentials then the request executes successfully.

So, how can I disable the windows authentication for my WEB API? thanks in advance.