Welcome to the wonderful world of troubleshooting.
"ceased working" is too broad of an expression...
... I'll find out if the host is alive
... I'll find out if the offending instance is alive
... I'll find out if "ceased working" for all apps or for a specific one
... I'll find out if there is connectivity to the host, instance.
SQL Server and O/S logs will come handy - depending on findings you can carry on.
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Pablo (Paul) Berzukov
Author of Understanding Database Administration available at Amazon and other bookstores.
Disclaimer: Advice is provided to the best of my knowledge but no implicit or explicit warranties are provided. Since the advisor explicitly encourages testing any and all suggestions on a test non-production environment advisor should not held liable or responsible for any actions taken based on the given advice.