I have an ArcGIS Server from Esri running and I need to check every hour if some published services (maps) are running. WMS and WFS.
Once you have that reference, use the Status property on the IServerObjectConfigurationStatus interface to check the status of the service. If the value is esriConfigurationStatus.esriCSStarted, then the service is started.
Then, it's just a matter of choosing the type of application you want to use to perform the check, whether a service or a scheduled application or a component of a larger application.