I think there is a problem with your web.config files.
Here my MVC 4 ext.net integrated application web.config file.
I hope it helps.
<?xml version="1.0" encoding="utf-8"?>
<configuration>
<configSections>
<!-- For more information on Entity Framework configuration, visit http://go.microsoft.com/fwlink/?LinkID=237468 -->
<section name="entityFramework" type="System.Data.Entity.Internal.ConfigFile.EntityFrameworkSection, EntityFramework, Version=5.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089" requirePermission="false" />
<section name="extnet" type="Ext.Net.GlobalConfig" requirePermission="false"/>
</configSections>
<extnet theme="Gray"/>
<connectionStrings>
<add name="DefaultConnection" providerName="System.Data.SqlClient" connectionString="Data Source=(LocalDb)\v11.0;Initial Catalog=aspnet-MVC4ExtNetTemplate-20130401120654;Integrated Security=SSPI;AttachDBFilename=|DataDirectory|\aspnet-MVC4ExtNetTemplate-20130401120654.mdf" />
</connectionStrings>
<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" />
</appSettings>
<system.web>
<httpRuntime targetFramework="4.5" />
<compilation debug="true" targetFramework="4.5" />
<authentication mode="Forms">
<forms loginUrl="~/Account/Login" timeout="2880" />
</authentication>
<pages>
<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="Ext.Net"/>
<add namespace="Ext.Net.MVC"/>
</namespaces>
</pages>
<profile defaultProvider="DefaultProfileProvider">
<providers>
<add name="DefaultProfileProvider" type="System.Web.Providers.DefaultProfileProvider, System.Web.Providers, Version=1.0.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35" connectionStringName="DefaultConnection" applicationName="/" />
</providers>
</profile>
<membership defaultProvider="DefaultMembershipProvider">
<providers>
<add name="DefaultMembershipProvider" type="System.Web.Providers.DefaultMembershipProvider, System.Web.Providers, Version=1.0.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35" connectionStringName="DefaultConnection" enablePasswordRetrieval="false" enablePasswordReset="true" requiresQuestionAndAnswer="false" requiresUniqueEmail="false" maxInvalidPasswordAttempts="5" minRequiredPasswordLength="6" minRequiredNonalphanumericCharacters="0" passwordAttemptWindow="10" applicationName="/" />
</providers>
</membership>
<roleManager defaultProvider="DefaultRoleProvider">
<providers>
<add name="DefaultRoleProvider" type="System.Web.Providers.DefaultRoleProvider, System.Web.Providers, Version=1.0.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35" connectionStringName="DefaultConnection" applicationName="/" />
</providers>
</roleManager>
<!--
If you are deploying to a cloud environment that has multiple web server instances,
you should change session state mode from "InProc" to "Custom". In addition,
change the connection string named "DefaultConnection" to connect to an instance
of SQL Server (including SQL Azure and SQL Compact) instead of to SQL Server Express.
-->
<sessionState mode="InProc" customProvider="DefaultSessionProvider">
<providers>
<add name="DefaultSessionProvider" type="System.Web.Providers.DefaultSessionStateProvider, System.Web.Providers, Version=1.0.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35" connectionStringName="DefaultConnection" />
</providers>
</sessionState>
<httpHandlers>
<add path="*/ext.axd" verb="*" type="Ext.Net.ResourceHandler" validate="false"/>
</httpHandlers>
<httpModules>
<add name="DirectRequestModule" type="Ext.Net.DirectRequestModule, Ext.Net"/>
</httpModules>
</system.web>
<system.webServer>
<validation validateIntegratedModeConfiguration="false" />
<modules>
<add name="DirectRequestModule" preCondition="managedHandler" type="Ext.Net.DirectRequestModule, Ext.Net"/>
</modules>
<handlers>
<remove name="ExtensionlessUrlHandler-ISAPI-4.0_32bit" />
<remove name="ExtensionlessUrlHandler-ISAPI-4.0_64bit" />
<remove name="ExtensionlessUrlHandler-Integrated-4.0" />
<add name="ExtensionlessUrlHandler-ISAPI-4.0_32bit" path="*." verb="GET,HEAD,POST,DEBUG,PUT,DELETE,PATCH,OPTIONS" modules="IsapiModule" scriptProcessor="%windir%\Microsoft.NET\Framework\v4.0.30319\aspnet_isapi.dll" preCondition="classicMode,runtimeVersionv4.0,bitness32" responseBufferLimit="0" />
<add name="ExtensionlessUrlHandler-ISAPI-4.0_64bit" path="*." verb="GET,HEAD,POST,DEBUG,PUT,DELETE,PATCH,OPTIONS" modules="IsapiModule" scriptProcessor="%windir%\Microsoft.NET\Framework64\v4.0.30319\aspnet_isapi.dll" preCondition="classicMode,runtimeVersionv4.0,bitness64" responseBufferLimit="0" />
<add name="ExtensionlessUrlHandler-Integrated-4.0" path="*." verb="GET,HEAD,POST,DEBUG,PUT,DELETE,PATCH,OPTIONS" type="System.Web.Handlers.TransferRequestHandler" preCondition="integratedMode,runtimeVersionv4.0" />
<add name="DirectRequestHandler" verb="*" path="*/ext.axd" preCondition="integratedMode" type="Ext.Net.ResourceHandler"/>
</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="1.0.0.0-4.0.0.0" 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>
</assemblyBinding>
</runtime>
<entityFramework>
<defaultConnectionFactory type="System.Data.Entity.Infrastructure.SqlConnectionFactory, EntityFramework" />
</entityFramework>
</configuration>
