Good that you didn't have a SQL Server dump file. And basically SQL Error Log entries are logged in Application log too.

Are you using Clustering with Always ON or just Always ON ?

First find the exact stop time of the SQL services from the error log. Note that stop time and check a bunch of log entries before that time.

Looks like we can find some clue from the system log. The system log you posted is not enough. It's better to go back a little bit. Can you post all the system log entries on that day before the SQL Server failure ? You can attach it as a text file.

Also check the same on the SQL\Application log file too i.e all the events before the SQL Server stop time (on that day).

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SQLBuddy

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SQLBuddy