I have recently installed version 10, and would like to use the personal version of SDE. I have installed sqlexpress via the installation wizard which installed SDE. Now when I try to "Add Spatial Database connection" however I get the following error. "Entry for SDE instance not found in services file".
You stated that you installed SQL Server Express, but you didn't mention if you created a geodatabase. Did you connect to the database server node in ArcCatalog as a database server administrator and create a geodatabase already? If not, there isn't any geodatabase to connect to so creating a Spatial Database Connection won't work.
See this topic for an overview of getting started with ArcSDE geodatabases in SQL Server Express.
Are you using an ArcView license? You cannot create new ArcSDE geodatabases with an ArcView license. When I've seen the New Geodatabase option inactive before it was usually due to the Desktop license level.