Last year our application was throwing this error when we knew for a fact the SQL server WAS up & online. We eventually traced it to a configuration in the application for a different SQL instance which no longer existed. Though we didn't use the feature the configuration was for, we had tested it, and it turned out that if the connection string is filled out the application did test the connection.

Look through the apps configuration area, config files if they exist and registry. Look for the string "ConnectionString."

This troubleshooting would be easier if Microsoft included the name if the instance it is unable to connect to in this error (hint hint).