FAST Search Server 2010 Configuration Wizard–“Database Validation Failed: Could not connect to the database. Check the database connection string, the database name and the port number to the database server”.

While your are running FAST Search Configuration Wizard. One thing may happen refer from this post.
http://jamesemann.wordpress.com/2011/07/20/fast-search-server-2010-configuration-wizarddatabase-validation-failed-could-not-connect-to-the-database-check-the-database-connection-string-the-database-name-and-the-port-number-to/

but enable user permission only dbcreator is enough.