IIS site blocks internet connection

I'm fighting this problem for some time.

When my ASP.NET MVC4 website starts to get served on my locally installed IIS (runs on port 8081, not 80!), internet connectivity gets blocked.
Just like that.

I'm confused because it is really strange.
It behaves like this:

• when the website is first started, I can browse any site
• only when the first page is served, connectivity fails
• stopping the website afterwards doesn't help
• stopping the IIS server afterwards doesn't help either (!)
• the connectivity problem affects ping as well
• when I perform logon/logoff or restart the computer, the connectivity is back
• by looking at the trace, I can't see anything blocked by windows firewall
• EDIT: everything behaves the same with windows firewall off

I tried to change binding from localhost:8081 to {my IP address}:8081, but it doesn't help.
Any clues?

EDIT

FYI, this is my web.config:

<?xml version="1.0" encoding="utf-8"?>
<configuration>
  <configSections>
    <section name="log4net" type="log4net.Config.Log4NetConfigurationSectionHandler, log4net" />
    <section name="plisani.medo" type="System.Configuration.NameValueSectionHandler, System, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089" />
  </configSections>
  <connectionStrings configSource="connectionStrings.config" />
  <location path="Account">
    <system.web>
      <authorization>
        <allow users="*" />
      </authorization>
    </system.web>
  </location>
  <location path="Content">
    <system.web>
      <authorization>
        <allow users="*" />
      </authorization>
    </system.web>
  </location>
  <location path="Images">
    <system.web>
      <authorization>
        <allow users="*" />
      </authorization>
    </system.web>
  </location>
  <appSettings>
    <add key="webpages:Version" value="2.0.0.0" />
    <add key="webpages:Enabled" value="false" />
    <add key="PreserveLoginUrl" value="true" />
    <add key="ClientValidationEnabled" value="true" />
    <add key="UnobtrusiveJavaScriptEnabled" value="true" />
    <add key="log4net.Internal.Debug" value="true" />
    <add key="MvcSiteMapProvider_UseExternalDIContainer" value="true" />
    <add key="MvcSiteMapProvider_SiteMapFileName" value="~/Mvc.sitemap" />
    <add key="MvcSiteMapProvider_IncludeAssembliesForScan" value="GeomarketingWeb" />
  </appSettings>
  <plisani.medo>
    <add key="zeko1" value="MYDOMAIN\xxxxxxxxxxxxxxxx" />
    <add key="zeko2" value="xxxxxxxxxxxxxxxx" />
  </plisani.medo>
  <system.diagnostics>
    <trace autoflush="true">
      <listeners>
        <add name="textWriterTraceListener" type="System.Diagnostics.TextWriterTraceListener" initializeData="Logs\log4netDebug.txt" />
      </listeners>
    </trace>
  </system.diagnostics>
  <system.web>
    <compilation debug="true" targetFramework="4.5" />
    <sessionState cookieName=".tempsession" 
                  cookieless="UseCookies" 
                  regenerateExpiredSessionId="true" 
                  mode="Custom" 
                  customProvider="SessionProvider">
      <providers>
        <add name="SessionProvider" 
             type="GeomarketingWeb.Providers.SessionProvider" 
             connectionStringName="GMDB" />
      </providers>
    </sessionState>
    <authentication mode="Forms">
      <forms loginUrl="~/Account/Logon" 
             name=".GMAUTH" 
             timeout="1440" 
             defaultUrl="~/Home/Index" 
             slidingExpiration="true" />
    </authentication>
    <authorization>
      <deny users="?" />
    </authorization>
    <membership defaultProvider="GeomarketingMembershipProvider">
      <providers>
        <clear />
        <add name="GeomarketingMembershipProvider" 
             type="System.Web.Security.ActiveDirectoryMembershipProvider" 
             connectionStringName="GMAD" 
             attributeMapUsername="sAMAccountName" 
             connectionUsername="" 
             connectionPassword="" 
             connectionProtection="Secure" 
             enablePasswordReset="false" 
             enableSearchMethods="true" 
             requiresQuestionAndAnswer="false" 
             requiresUniqueEmail="false" 
             maxInvalidPasswordAttempts="5" 
             minRequiredPasswordLength="6" 
             minRequiredNonalphanumericCharacters="0" 
             passwordAttemptWindow="10" 
             applicationName="Geomarketing" />
      </providers>
    </membership>
    <roleManager defaultProvider="GeomarketingRoleProvider" enabled="true" cacheRolesInCookie="true" cookieName=".GMROLES" cookieTimeout="5" cookiePath="/" cookieSlidingExpiration="true">
      <providers>
        <clear />
        <add name="GeomarketingRoleProvider" type="GeomarketingWeb.Providers.RoleProvider" connectionStringName="GMDB" applicationName="Geomarketing" />
      </providers>
    </roleManager>
    <profile defaultProvider="DefaultProfileProvider">
      <providers>
        <add name="DefaultProfileProvider" 
             type="System.Web.Providers.DefaultProfileProvider" 
             connectionStringName="DefaultConnection" 
             applicationname="Geomarketing" />
      </providers>
    </profile>
    <pages controlRenderingCompatibilityVersion="4.0">
      <namespaces>
        <add namespace="System.Web.Helpers" />
        <add namespace="System.Web.Mvc" />
        <add namespace="System.Web.Mvc.Ajax" />
        <add namespace="System.Web.Mvc.Html" />
        <add namespace="System.Web.Optimization" />
        <add namespace="System.Web.Routing" />
        <add namespace="System.Web.WebPages" />
        <add namespace="MvcSiteMapProvider.Web.Html" />
        <add namespace="MvcSiteMapProvider.Web.Html.Models" />
      </namespaces>
    </pages>
  </system.web>
  <system.webServer>
    <validation validateIntegratedModeConfiguration="true" />
    <modules runAllManagedModulesForAllRequests="true" />
    <handlers>
      <remove name="ExtensionlessUrlHandler-Integrated-4.0" />
      <add name="ExtensionlessUrlHandler-Integrated-4.0" 
           path="*." 
           verb="*" 
           type="System.Web.Handlers.TransferRequestHandler" 
           resourceType="Unspecified"
           requireAccess="Script"
           preCondition="integratedMode,runtimeVersionv4.0" />
    </handlers>
  </system.webServer>
  <runtime>
    <assemblyBinding xmlns="urn:schemas-microsoft-com:asm.v1">
      <dependentAssembly>
        <assemblyIdentity name="System.Web.Helpers" publicKeyToken="31bf3856ad364e35" />
        <bindingRedirect oldVersion="1.0.0.0-2.0.0.0" newVersion="2.0.0.0" />
      </dependentAssembly>
      <dependentAssembly>
        <assemblyIdentity name="System.Web.Mvc" publicKeyToken="31bf3856ad364e35" />
        <bindingRedirect oldVersion="0.0.0.0-4.0.0.0" newVersion="4.0.0.0" />
      </dependentAssembly>
      <dependentAssembly>
        <assemblyIdentity name="System.Web.WebPages" publicKeyToken="31bf3856ad364e35" />
        <bindingRedirect oldVersion="1.0.0.0-2.0.0.0" newVersion="2.0.0.0" />
      </dependentAssembly>
      <dependentAssembly>
        <assemblyIdentity name="System.Web.Http" publicKeyToken="31bf3856ad364e35" culture="neutral" />
        <bindingRedirect oldVersion="0.0.0.0-5.1.0.0" newVersion="5.1.0.0" />
      </dependentAssembly>
      <dependentAssembly>
        <assemblyIdentity name="System.Net.Http.Formatting" publicKeyToken="31bf3856ad364e35" culture="neutral" />
        <bindingRedirect oldVersion="0.0.0.0-5.0.0.0" newVersion="5.0.0.0" />
      </dependentAssembly>
    </assemblyBinding>
  </runtime>
</configuration>