If you want to install BlogEngine.NET or any other web application in a virtual directory (or subdirectory) underneath a DotNetNuke installation, you'll have to make sure, that the configuration settings of DotNetNuke are not inherited by BlogEngine.Net. In order to prevent this, you need to change the web.config file of DotNetNuke and surround the <system.web> part with the following tag:

<location path="." inheritInChildApplications="false">
  <system.web>
    ...
  </system.web>
</location>