This error can mean a few different things. I will go over a few typical fixes for this issue.
One possibility is the need to update an INI file for Genesis. This file is found in 'C:\Program Files (x86)\Esha Research\GenesisSQL\'. If Windows 7 or Vista, this can also be found in 'C:\Users\[UserProfile]\AppData\Local\VirtualStore\Program Files (x86)\Esha Research\GenesisSQL\'. If both files exist, make the change in both INI files.
You will also want to check the ServerName= line and make sure that the name of your server is correct and check to make sure the line Provider= is correct. For a network install it will need to be Provider=SQLOLEDB.1 and for a local install you will need Provider=SQLNCLI11
This error also happens when you do not have permissions to access the database. This Knowledge Base article details how to grant users permission to the database.