OK!
User instances are possible on MSSQL express edition only, so you cannot have .\SQLEXPRESS in LocalSQLServer connection string in your c:\windows\Microsoft.Net\Framework\v2.0.50727maching.config
You need that connection string to be valid to doASP.NET authentication.
Resolution is as follows:
First run aspnet_regsql.exe command-line tool (in c:\windows\Microsoft.Net\Framework\v2.0.50727) and it will create a database on your MSSQL (developer, standard... edition) server. The name of database is aspnetdb.
Next, change the connection string 'LocalSqlServer' in your c:\windows\Microsoft.Net\Framework\v2.0.50727\maching.config to:
<add name="LocalSqlServer" connectionString="Data Source=MYSERVERNAME;Initial Catalog=aspnetdb;Integrated Security=True" providerName="System.Data.SqlClient" />
Do not forget to change MYSERVERNAME in connection string