How do I enable HTTP PUT and DELETE for ASP.NET MVC in IIS?

Go to Handler Mappings in your IIS Manager. Find ExtensionlessUrlHandler-Integrated-4.0, double click it. Click Request Restrictions… button and on Verbs tab, add both DELETE and PUT.

Possible WebDav Publisher issue

You’ve mention on a deleted post you were running on a 2008 server right? Try removing webDav role, or disable it from your site config: on system.webServer -> modules section, remove WebDAVModule module:

<system.webServer>
  <modules>
    <remove name="WebDAVModule" />
  </modules>
  <handlers>
    <remove name="WebDAV" />
  </handlers>
</system.webServer>