Issue
If you can't connect to the search service and have verified ElasticSearch is running, check the application log file found in Admin > Errors & Logging.
If you see an error message which contains "IndexMissingException" as shown below, it's likely the current application name set in Intranet/Admin/cfregdn.cfm is different that it was before, and it's this name which is used as the index name in ElasticSearch.
2016/06/02 08:59:02.10,intranet.sqbox.controllers.Search,ERROR - Unknown Error: Unknown Error
detail: Body: {"error":"IndexMissingException[[intranetconnections] missing]","status":404}
Resolution
On the web server, in a browser enter address:
http://localhost:9200/_cat/indicies?v
In the return results, find the second value on the second line, which is the index name. The default is "sqbox".
Edit the Intranet/Admin/cfregdn.cfm file and set ApplicationName to match the index name.
After saving changes, restart the application by clicking [restart] beside the application name (default is SQBOX) in the center column at the bottom of the Admin > Setup screen.