You either need to provide a SQL username and password in your connection string like this:
<connectionstrings>
<add name="MyConString" connectionstring="Data Source=serverName;Initial Catalog=dbName;Persist Security Info=True;User ID=someUserId;Password=usersPassword" providername="System.Data.SqlClient" />
</connectionstrings>
or, keep the connection string you have but change the account being used on your application pool in IIS to an account that has sufficient privileges in SQL.