Can't connect to membership tables in our database

Question

We used the aspnet_regsql.exe tool to add membership tables to our existing database and added the following LocalSqlServer lines into our Web.config file:

<clear/>

<add name="Dorknozzle"
     connectionString="Server=OUR-PC;Database=Dorknozzle;Integrated Security=True"
     providerName="System.Data.SqlClient" />

<add name="LocalSqlServer"
    connectionString="Server=OUR-PC;Database=Dorknozzle;Integrated Security=True"
    providerName="System.Data.SqlClient" />

When we click on the Security tab of the Web Site Administration Tool we get the following error:

There is a problem with your selected data store.

The server and database names are correct because the web forms do display data from the Dorknozzle database and I made sure that the membership tables are residing in the Dorknozzle database.

We also clicked on the Provider tab but could only see AspNetSqlProvider when we were expecting to also see Dorknozzle.

Can you tell me what we are missing to get the Web Site Administration Tool to connect to the data store in dorknozzle?

Update: Thanks go to Jon for guiding us with this issue. I added the following codeing in the system.web section of our Web.config file and we can now see the information in the Security tab of the Web Site Administration Tool:

<membership>
  <providers>
    <clear />
    <add name="AspNetSqlMembershipProvider" 
         type="System.Web.Security.SqlMembershipProvider"
         connectionStringName="Dorknozzle" 
         enablePasswordRetrieval="false" 
         enablePasswordReset="true"
         requiresQuestionAndAnswer="false" 
         requiresUniqueEmail="false" 
         maxInvalidPasswordAttempts="5"
         minRequiredPasswordLength="6" 
         minRequiredNonalphanumericCharacters="0" 
         passwordAttemptWindow="10" 
         applicationName="/" />
  </providers>
</membership>