Running SQL Server Express on Amazon EC2 Windows instance

I created a Windows Server 2008 Amazon EC2 instance with IIS and SQL Server Express pre-installed (using this AMI http://aws.amazon.com/amis/Microsoft-Windows/4801904273096347). After logging in I fired up SQL Management Studio and attempted to log into the default instance (Database Engine) using Windows Authentication. I was unsuccessful. I get an error message that says the service may not be running...I double checked to ensure that it was indeed running.

Has anyone setup SQL Server Express using an Amazon EC2 instance? Am I better off using a base Windows Server 2008 instance and installing SQL server from scratch? Do I need to create a user?

Ok so to get this to work properly I ensured all of the SQL Services were running (via the Services MMC) and then had to use SQL Management Studio to connect to the .\EC2SQLEXPRESS instance. Previously I was trying to use the management studio to connect to the default instance (i.e., the machine name).