Hi Kevin
You are correct - SCOM should generate an alert when a windows server is down. There are 2 specific alerts, both of which as ENABLED by default:
- Health Service Heartbeat Failure
- Failed to Connect to Computer
They are discussed in detail here:
http://blogs.technet.com/b/jonathanalmquist/archive/2010/01/11/health-service-heartbeat-failure-diagnostics-and-recoveries.aspx
Just a quick check on terminology - is there definitely no alert in the alerts view? Perhaps start the server again, wait for health state to go green and then shut it down and check to see if you get the above alerts. If you close these alerts then they
will disappear and not re-appear again as the alert is generated by a monitor:
http://www.culham.net/scom/scom-rules-vs-monitors/
If you are looking at notifications e.g. an email when the server goes down then you have a couple of options. To check everything works, I'd create a subscription for the specific monitors mentioned above. In the long term, you probably want to create
groups of health service watcher objects - this is the object that actually fires the alert (it isn't the "server" itself).
http://blogs.technet.com/b/kevinholman/archive/2014/04/09/creating-groups-of-health-service-watcher-objects-based-on-other-groups.aspx
Cheers
Graham