Try to use SQL Management Studio logged in as the K2 Service Account and attempt to connect to the specific DB Instance and Database to make sure you have permissions and connectivity setup correctly.
I'm thinking either is a typo error or permissions error on the Database name. perphas you are using a SQL Alias and is pointing to the wrong reference. but surely if can connect using the SQL Mgmt Studio you should be able to connect from the K2 Tester.
Other idea is make sure you don't have any software firewall blocking the connection somehow.
Hope this helps.
Has this been resolved? In the service keys section did you set the field "On Different SQL Server - Required" to true? You said it was able to connect to the server just fine but did not recognize the database. Was the database specified in the "Database - Required" field? There could be a typo in the database name.
Thanks,
Bryan Peters