I do not know if there are any issues with your configuration, but I have some suggestions for troubleshooting. Maybe they will help you arrive at the cause of the issue.
1. Check that your SQL express instance has been set up properly. For example, can you launch SQL Server Management Studio and connect using Windows Authentication as SysAdmin? Normally this works but it is worthwhile to confirm.
2. Another test would be to configure a new user in SQL Express with SQL Authentication. Grant this user Admin rights in SQL. Then configure SiteFinity to user this other user. Go to the DataConfig.config file in \\your project name\App_Data\Sitefinity\Configuration. Edit the connection string to use your new login
<add connectionString="data source=ALANSWINBOX;uid=alan;PWD=1234;initial catalog=SiteFInityDBName " providerName="System.Data.SqlClient" dbType="msSql" name ="SiteFinity" />
3) Reset IIS and then run your test again to see what happens. If you get the same error message then ignore authentication as this isn't the issue